Philosophical Transactions/Volume 1/Number 4

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Numb. 4



Munday, June 5. 1665.

The Contents.

A Relation of some extraordinary Tydes in the West-Isles of Scotland, by Sr. Robert Moray.The judgment of Monsieur Auzout, touching the Apertures of Object-glasses, and their proportions in respect of the several lengths of Telescopes; together with a Table thereof.Considerations of the same Person upon Mr. Hook's New Engine for grinding of Optick-Glasses.Mr. Hook's Thoughts thereupon.Of a means to illuminate an Object in what proportion one pleaseth; and of the distances, that are requisite to burn Bodies by the Sun.A further accompt by Monsieur Auzout of Signior Campani’s Book, and performances about Optick-Glasses.Campani’s Answer thereunto; and Mr. Auzout’s Animadversions upon that Answer.An accompt of Mr. Lower’s newly published Vindication of Dr. Willis’s Diatriba de Febribus.

A Relation of some extraordinary Tydes in the West-Isles of Scotland, as it was communicated by Sr. Robert Moray.

Phil Trans - Illuminated Capital - I.pngN that Tract of Isles, on the West of Scotland, called by the Inhabitants, the Long-Island, as being about 100 miles long from North to South, there is a multitude of small islands, situated in a Fretum, or Frith, that passes between the Island of Eust, and the Herris; amongst which, there is one called Berneray, some three miles long, and more than a mile broad, the length running from East to West, as the Frith lyes. At the East end of this Island, where I stayed some 16. or 17. dayes, I observed a very strange Reciprocation of the Flux and Reflux of the Sea, and heard of another, no less remarkable.

Upon the West side of the Long Island, the Tides, which came from the South-west, run along the Coast, Northward; so that during the ordinary course of the Tides, the Flood runs East in the Frith, where Berneray lyes, and the Ebb West. And thus the Sea ebbs and flows orderly, some 4. days before the full Moon, and change, and as long after (the ordinary Spring-tides rising some 14. or 15. foot upright, and all the rest proportionably, as in other places. But afterwards, some 4. days before the Quarter moons, and as long after, there is constantly a great and singular variation. For then, (as Southerly Moon making there the full Sea) the course of the Tide being Eastward, when it begins to flow, which is about 91/2 of the Clock, not onely connues so till about 31/2 in the afternoon, that it be high water, but, after it begins to ebb, the Current runs on still Eastward, during the whole Ebbs so that it runs Eastward 12 hours together, that is, all day long, from about 91/2 in the morning, til about 91/2 at night. But then, when the night-Tide begins to flow, the Current turns, and runs Westward all night, during both Floud & Ebb, for some 12 hours more, as it did Eastward the day before. And thus the Reciprocations continue, one Floud and Ebb, running 12. hours Eastward, and another twelve hours Westward, till 4. days before the New and Full Moon; and then they resume their ordinary regular course as before, running East, during the six hours of Floud, and West, during the six of Ebb. And this I observed curiously, during my abode upon the place, which was in the Moneth of August, as I remember.

But the Gentleman, to whom the Island belongs at present, and divers of his Brothers and Friends, knowing and discreet persons, and expert in all such parts of Sea-matters, as other Islanders commonly are, though I shrewdly suspected their skill in Tides, when I had not yet seen what they told me, and I have now related of these irregular Courses of the Tides, did most confidently assure me, and so did every body I spake with about it, that there is yet another irregularity in the Tides, which never fails, and is no less extraordinary, than what I have been mentioning: which is, that, whereas between the Vernal and Autumnal Equinoxes, that is, for six Moneths together, the Course of irregular Tides about the Quartermoons, is, to run all day, that is, twelve hours, as from about 91/2 to 91/2, 101/4 to 101/4 &c. Eastward, and all night, that is, twelve hours more, Westward: during the other six Moneths, from the Autumnal to the Vernal Equinox, the Current runs all day Westward, and all Night Eastward.

Of this, though I had not the opportunity to be an Eye-witness, as of the other, yet I do not at all doubt, having received so credible Information of it.

To penetrate into the Causes of these: strange Reciprocations of the Tides, would require exact descriptions of the Situation, Shape, and Extent of every piece of the adjacent Coasts of Eust and Herris; the Rocks, Sands, Shelves, Promontorys, Bays, Lakes, Depths, and other Circumstances, which I cannot now set down with any certainty, or accurateness; seeing, they are to be found in no Map, neither had I any opportunity to survey them; nor do they now occur to my Memory, as they did some years ago, when upon occasion I ventured to make a Map of this whole Frith of Berneray, which not having copied. I cannot adventure to beat it out again.


Monsieur Azout's judgment touching the Apertures of Object-glasses, 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 LAbbe Charles; That great Optick Glasses 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 the Reader, that he hath found, that the Apertures, which Optick Glasses 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-Glasses.
The points put to some of these Number denote Fractions.
Lengths of
For excellent
For good
For ordinary
Lengths of
For excellent
For good
For ordinary
Feet, Inches. Inch. Lines. Inch. Lines. Inch. Lines. Feet, Inches. Inch. Lines. Inch. Lines. Inch. Lines.
4 4. 4 3 25 3 4 2 10 2 4.
6 5. 5 4 30 3 8 3 2 2 7.
9 7 6. 5 35 4 0 3 4 2 10
1 0 8. 7 6 40 4 3 3 7 3 .
1 6 9 8. 7 45 4 6 3 10 3 2
2 0 11 10 8 50 4 9 4 0 3 4.
2 6 1 0 11 9 55 5 0 4 3 3 6.
3 0 1 1 1 0 10 60 5 2 4 6 3 8.
3 6 1 2 1 1 11 65 5 4 4 8 3 10
4 0 1 4 1 2 1 0 70 5 7 4 10 4 .
4 6 1 5 1 3 1 . 75 5 9 5 0 4 2.
5 0 1 6 1 4 1 1. 80 5 11 5 2 4 5
6 1 7. 1 5 1 2 90 6 4 5 6 4 7.
7 1 9 1 6 1 3 100 6 8 5 9 4 10
8 1 10 1 8 1 4 120 7 5 6 5 5 3
9 1 11 1 9 1 5 150 8 0 7 0 5 11
10 2 1 1 10 1 6 200 9 6 8 0 6 9
12 2 4 2 0 1 8 250 10 6 9 2 7 8.
14 2 6 2 2 1 9. 300 11 6 10 0 8 5
16 2 8 2 4 1 11. 350 12 6. 10 9 9 0
18 2 10 2 6 2 1 400 13 4 11 6 9 8
20 3 0 2 7 2 2.

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 Optic-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 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 exceeding 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[errata 1]; 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 he judged what piece of Glass, and of what thickness it must be, to endure[errata 2] 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[errata 3] two Mandrils could be put in one and the same plain[errata 4], & 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 become 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[errata 5] 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 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 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 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 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 Method, he knows, of finding out as much in Mechanics, 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 Aperture, 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 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 fends 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 smallnes 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, howl could they make us see some of the fiftieth, and it may be some of the hundreth, and two hundreth Magnitude, as they do, and as they would shew yet much lesser ones, if they. did magnifie more?

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


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 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 with 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 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 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 my self 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 Tools; One, &c. And if curiosity shall ever proceed so farr, one for all lengths, between 100 and 10000 feet long, for indeed, the Principle is such, that 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 Obections 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 Azout, that it may be a very 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 Animadversor saw a long Glass, 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-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 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 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 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 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 Glass so made shall draw, is not so easie: 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 steddy, when once fix'd, is most easie.

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 Ey-glass 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 Glass can be made of any Sphere between twenty and fourty 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, not withstanding 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 diistance: 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 diffident 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 conteined as wel 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 weigh, 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.

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. Auzout seems to find fault with the English Glass of 36 foot, that had an Aperture of but 23/4 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. Auzout to enlighten an Object, in what proportion one pleaseth, is by some great Object-Glass, 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 tor 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 Glass it did not sensibly appear so; Whereof he promises to discourse more fully in his Treatise of the usefulness of great Optick-Glasses, where he also intends to deliver several Experiments, by him made, 1. Touching the quantity 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 quantity of Light, by which the Earth is illuminated even in the Eclipses of the Sun, in proportion of their bigness. 3. Touching the quantity of Light, which is necessary to burn Bodies: he having found, that not abating the Light, which is reflected by the Surfaces of the Glass (whereof he confesseth, he doth not yet exactly know the quantity) 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 Glasses and great Looking-glasses. 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-glasses, with how much less Aperture they will burn there, than here, to know from thence, whether there be 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 quantity of Light, at least that of the Heat found there.

A further Account, touching Signor Campani’s Book and Performances about Optic-glasses.

In the above-mentioned French Tract there is also contained 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 his New Observations of Saturn and Jupiter, made by means thereof.

First therefore, after that M. Auzout had raised some scruple against the Contrivance of Signor Campani for making Great Optick-Glasses without Moulds, by the means of a Turn-lath, he examines the Observations, made with such Glasses: Where, having commended Campani’s sincerity in relating what he thought to have seen in Saturn, without accommodating it to M. Hugen's Hypothesis, he affirms, that supposing, there be a Ring about Saturn, Signor Campani could not see in all those different times, that he observed it, the same Appearances, which he notes to have actually seen. For, having seen it sometimes in Trine Aspect with the Sun, and Oriental; sometimes, in the same Aspect, but Occidental; sometimes in Sextil Aspect, and Occidental, at another time, again in Trine and Oriental, this Author cannot conceive, how Saturn could in all these different times have no difference in its Phasis, or keep always the same Shadow; seeing that, according to the Hypothesis of the Ring, when it was Oriental, it must cast the Shadow upon the left side of the Ring beneath, without casting any on the right side; and when it was Occidental, it could not but cast it on the right side beneath, and nothing of it on the other.

Concerning the Shadow above, which Campani affirms to be made by the Ring upon the Body of Saturn, M. Auzout judges, that there could be no such Phænomenon, by reason of its Northern Latitude at the times, wherein the Observations were made, vid. in April 1663; in the midst of August, and the beginning of October, next following, and in April 1664, except it were in October, and the Shadow strong enough to become visible.

But as to the shadow below, he agrees with Campani, that it does appear, yet not as he notes it, seeing that it must be sometimes on the one side, sometimes on the other; and towards the Quadrat with the Sun it must appear biggest, as indeed he affirms to have seen it himself this year, insomuch that sometimes it seemed to him, that it covered the whole Ring, and that the Shadow, joyning with the obscure space between both, did interrupt the circumference of the Ring; but beholding it at other times in a cleer Sky, and when there was no Trepidation of the Air, he thought, that he saw also the Light continued from without, although very slender. But he acknowledges, that he could never yet precisely determine, by how much the largeness of the Ring was bigger than the Diameter of Saturn's Body. As for the proportion of the Length to the Breadth, he affirms, to have alwaies estimated it to be two and a half, or very neer so; and to have found in his Observations, that in January last, one time, the length of Saturn was 12 Lines, and the breadth 5. Another time, the length was 12. Lines, and the breadth 4. and this by a peculiar method of his own. But yet he acknowledges also, that sometimes he hath estimated it as 7, to 3. and at other times as 13. to 5. and that if there do not happen a change in the magnitude of the Ring (as it is not likely there does) that must needs proceed from the Constitution of the air, or of the Glass's having more or less Aperture, or from the difficulty of making an exact estimate of their proportions. However it is not much wide (saith he) of two and an half, although Campani make the length of the Ring but double to its breadth.

Monsieur Auzout believes, that he was one of the first that have well observed this shadow of Saturn’s Body upon its Rings which he affirms happened two years since; when, observing in July, for the first time, with a Telescope of 21. and then another of 27. foot, he perceived, that the Angle of the obscure space on the right side beneath, was bigger and wider, than the three other Angles, and that some interruption appear'd there, between the Ring, and the Body of Saturn; of which he saith to have given notice from that time to all his friends, and in particular, as soon as conveniently he could, to Monsieur Hugens.

He confesseth, that he hath not had the opportunity of observing Saturn in his Oriental Quadrat; yet he doubts not, but that the shadow appears on the Left-side, considering, that the Existence of the Ring can be no longer doubted of, after so many Observations of the shadow cast by Saturn’s Body upon it, according as it must happen, following that Hypothesis; there being no reason, why it should cast the said shadow on one side, and not on the other.

Concerning the Observation of Jupiter and its satellites, the famous Astronomer of Bononia, Cassinus, having published, that on the 30. day of July, 1664. at 21/2 of the clock in the morning, he had observ'd, with Campani’s Glasses, that there passed through the broad obscure Belt of Jupiter two obscurer spots, by him esteemed to be the shadows of the Satellites, moving between Jupiter & the Sun, and eclipsing him, and emerging from the Occidental Brim thereof: This Authour did first conceive, that they were not shadows, but some Sallies, or Prominencies in that Belt; which he was induced to believe, because he perceived not, that that Prominency, which he there saw was so black, nor so round as Cassini had represented his spots; wherefore, seeing it but little differing in colour, from the Belt, and so not judging it round, because it did stand only about half its diameter out of the Belt, he persuaded himself, that it was rather a Sally, or Prominency of the Belt, than a round shadow, as that of a Satellite of Jupiter must have bin. But having been since informed of all the Observations made by Cassini and Campani, with the New Glasses, and seen his Figure, he candidly and publickly wisheth, that he had not spoken of that Sally, or Prominency; advowing that he can doubt no longer, but that it was the shadow of the Satellit between Jupiter and the Sun, having seen the other emerge, as soon as with a 20. foot Glass he made the Observation, and having not perceiv'd these shadows with a 12. foot Glass: But although he grants that they did ghess better than he, yet he doth it with this proviso, vid. in case they made that Observation of July 30. not with their 36. but 12. or 17. foot Telescope. If it be wondred at, that Monsieur Auzout did not see this shadow move, he allegeth his indisposition for making long Observations, and addeth, that it may be much more wondred at, that neither Campani nor himself did see upon the obscure Belt the Bodies of the Satellites, as parts more Luminous than the Belt. For (saith he) although the Latitude was Meridional, it being no more than of 9. or 10. minutes, the Body of the Satellites should, thinks he, pass between us and the Belt, especially according to Campani, who maketh the Belt so large, and puts the shadows farr enough within the same. This maketh him conclude, that either they have not observed well enough, or that the motion of the Satellites doth not exactly follow the Belts, and is inclin'd unto them. Whereupon he revolves, that when he shall know that they are to pass between Jupiter and us, and to be over against the Belt, that then he will observe, whether he can see them appear upon the Belt, as upon a darker ground, especially, the third of them, which is sensibly greater, and more Luminous, than the rest. He hopeth also, that in time, the shadow of Saturns Moon will be seen upon Saturn, although we are yet some years to stay for it, and to prepare also for better Glasses.

From this rare Observation, he inferrs the Proportion of the Diameter of the Satellites to that of Jupiter; and judgeth, that no longer doubt can be made of the turning of these 4. Satellites, or Moons about Jupiter, as our Moon turns about the Earth, and after the same way as the rest of the Celestial Bodies of our Systeme do move: whence also a strong conjecture may be made, that Saturns Moon turns likewise about Saturn.

Hence he also taketh occasion to intimate, that we need not scruple to conclude, that if these two Planets have Moons wheeling about them, as our Earth hath one that moves about it, the conformity of these Moons with our Moon, does prove the conformity of our Earth with those Planets, which carrying away their Moons with themselves, do turn about the Sun, and very probably make their Moons turn about them in turning themselves about their Axis; and also, that there is no cause to invent perplex'd and incredible Hypotheses, for the receding from this Analogie since (saith he) if this be truth, the Prohibitions of publishing this doctrine, which formerly were caused by the offence of Novelty, will be laid aside, as one of the most: zealous Doctors of the contrary Opinion hath given cause to hope, witness Eustachius de Divinis, in his Tract against Monsieur Hugen's Systeme of Saturn, p. 49. where we are inform'd, that that learned Jesuit, P. Fabry, Penitentiary of S Peter in Rome, speaks to this purpose:

* Ex vellris, iifque Coryphæis non femel quæfitum est, utrum aliquam haberent demonstrationem pro Terræ motu adstruendo. Nunquam ausi sunt id afferrre elbutrum Nligitur obstat qui loca illa in sensu literali Ecclesia intelligat, & intelligenda esse declaret, quamdiu nulla demonstratione contrarium evincitur; quæ si forte aliquando à vobis excogitur (quod vix crediderim) in hoc casu nullo modo dubitabit Ecclesia declarare, loca illa in sensu figurato & imporprio intelligenda effe, ur illud Poetæ, Terræque Urbesque recedunt.
* It hath been more than once asked of your Chieftains, whether they had a Demonstration for asserting the motion of the Earth? They durst never yet affirm they had, wherefore nothing hinders, but that that Church may understand those Scripture-places, that speak of this matter, in a literal sence, and declare they should be so understood, as long as the contrary is not evinced by any demonstrations;

Whence this Author concludes, that the said Jesuite assuring us that the inquisition hath not absolutely declared, that those Scripture places are to be understood literally, seeing that the Church may make a contrary declaration, no man ought to scruple to follow the Hypothesis of the Earths motion, but only forbear to maintain it in publick, till the prohibition be called in. But to return to the matter in hand, this Author upon all these observations and relations of Cassini and Campani, doth find no reason to doubt any more of the excellency of the Glass used by them, above his; except this difference may be imputed to that of the Air, or of the Eys. But yet he is rather inclined to ascribe it to the goodness of their Glasses, and that the rather, because, he would not be thought to have the vanity of magnifying his own; of which, yet he intimates by the by, that he caused one to be wrought, of 150 Parisian feet; which though it proved none of the best, yet he despairs not to make good ones of that, and of far greater Length.


Signor Campani's Answer: and Monsieur Auzout’s Animadversions thereon.

The other part of this French Tract, conteining Campani’s Answer, and Mr. Auzout his Reflections thereon, begins with the pretended Shadows of the Ring upon Saturn, and of Saturn upon the Ring. Concerning which, the said Campani declareth, that he never believed them as shadows, made by the Ring upon the Disk of Saturn, or by the body of Saturn upon the Ring, but the Rimms of these bodies, which being unequally Luminous, did shew these appearances. In which Explication, for as much it represents, that the said Campani meant to note only the Inequality of the Light, which, he saith, his Glasses did discover, Mr. Auzout does so far acquiesce, that he only wishes, that his own Glasses would shew him those differences. Next to the Objection, made by Monsieur Auzout, against Signor Campani, touching the Proportion of the Length of the Ring to its breadth, Campani replyeth, that the Glasses of Monsieur Auzout, shew not all the particulars, that his do, and therefore are unfit for determining the true Figure and breadth of the apparent Ellipsis of the Ring. To which M. Auzout rejoyns, that he is displeased at his being destitute of better Glasses, but that it will be very hard for the future to convince Campani touching the Proportion of the Ring, seing that the breadth of the Ellipsis is always diminishing, although, if the declination of the Ring remains always the same, one can at all times know, which may have been its greatest breadth. But he assures, that the breadth of the Ring is not the half of its length, and that it doth not spread out so much beyond Saturn’s Body, as he hath alleged. And withal desirs to know, what can be answered by Sig. Campani to M. Hugens who being persuaded, that the Declination of the Ring is not above 23 deg. 30′ having seen the Ring to spread out above the Body of Saturn, concludes, in a Letter to M. Auzout, that the length of the Ring is more than treble the Diameter of Saturn’s body, which, according to Campani, is only as about 67 to 31. Which difference yet dos not appear to M. Auzout to be so great; but that M. Hugens perhaps will impure it to the Optical reason, which he (Auzout) hath alleged of the Advance of the light upon the obscure space; although he is of Opinion, he should not have concluded so great a Length, if he had not seen the Breadth spread out more, than he hath done: for (saith he) if the Length of the Ring be to the body of Saturn, as 21/2 to 1. and the Inclination be 23 deg. 30′ the Ring will be just as large, as the body, without spreading out; but if the Ring be bigger, it will a little spread out; and if it were treble, it must needs spread out the half of its breadth, which hath not so appeared to him.

Further, to M. Auzout's change of Opinion, and believing that the Advance or Sally, seen by him in Jupiter, was the shadow of one of his Moons, Campani declares, that he would not have him guilty of that change: Whereupon M. Auzout wonders, why Campani then hath not marked it in his Figure; and would gladly know, whether that Sally be more easie to discover, than the shadows of the Satellites, which Campani believs, Auzout hath not seen; and whether he be assured, that those obscure parts, which he there distinguishes, do not change: for if they should not change, then Jupiter would not turn about his Axis, which yet, he saith, it doth, according to the Observation made by Mr. Hook, May 9 1664. inserted in the first papers of these Transactions. The full Discovery of which particular also he makes to be a part of Cassini and Campani's work, seeing that they so distinctly see the inequalities in the Belts, and see also sometimes other Spots besides the shadows of the Satellites: where he exhorts all the Curious, that have the conveniency of observing, to endeavor the discovery of a matter of that importance, which would prove one of the greatest Analogies for the Earth's Motion.


An Account of Mr. Richard Lower's newly published Vindication of Doctor Willis's Diatriba de Febribus.

The Title of this Curious piece, is, Diatribæ Themæ Willisi Med. Doct. & Profess. Oxon. De Febribus Vindicatio, Authore Richardo Lower, &c. In it are occasionally discussed many considerable Medical and Anatomical inquiries, as, Whether a Fever does consist in an Effervescence of Blood? And if so, of what kind? Whether there be a Nervous and Nutritous Juice? Whether the office of sanguification belongs to the Blood it self, existing before those Viscera (at least) that are commonly esteemed to be the Organs of sanguification? How Nutrition is performed, and the nourishing substance assimilated? Whether the Blood affords both the Matter for the structure of the Body, and such parts also, as are fit for the nourishment of the same? Whether the Pulse of the Heart ceasing, there remains yet a certain Motion in the blood, arguing, that Pulse and Life do ultimately rest in the Blood? Whether the Umbilical Vessels convey the blood of the Mother to the Child, or whether the Fœtus be for the most part form'd and acted by the circulating blood, before the existence of the Umbilical Vessels, or before the connecting of the Fœtus with the Uterus? A new Experiment to prove, that the Chyle is not transmuted into Blood by the Liver. A discourse of the Nature of the Blood, and what difference there is between the Venal and Arterial blood, and for what Uses both the one and the other are particularly designed. Where it is considered, what Life is, and whence the Soul of Brutes, and its subsistence, and operations do depend. It is also inquired into, what the uses of the Lungs are in hot Animals? And many other such material disquisitions are to be found in this small, but very Ingenious and Learned Treatise.


A Note touching a Relation, inserted in the last Transactions.

In the Experiment of killing Ratle-Snakes, mentioned in the last of the precedent Papers (wherein, by a mistake, these words, The way, were put for A way, or An Experiment) it should have been added, that the Gentleman there mention'd, did affirm, that, in those places, where the Wild Penny-Royal or Dittany grows, no Ratle-Snakes are observed to come.


Pag. 59. line 11. read, bignesses, l. 20. r. endure, for, resist. l. 30. r. those, for, these, l. 31. r. Plain, for, place.



Printed with Licence, By John Martyn, and James Allestry, Printers to the Royal-Society, at the Bell in St. Pauls Church-Yard. 1665.


  1. Original: bigness was amended to bignesses: detail
  2. Original: resist was amended to endure: detail
  3. Original: these was amended to those: detail
  4. Original: place was amended to plain: detail
  5. Original: hundred was amended to eight: detail