Book XVII, chapters 11–17: Burning-glasses and wonderful sights

CHAP. XI.

Of Spectacles whereby one may see very far, beyond imagination.

I Will not omit a thing admirable and exceeding useful; how bleare-ey'd people may see very far, and beyond that one would believe. I spake of Plotomies Glass, or rather spectacle, whereby for six hundred miles he saw the enemies ships coming; and I shall attempt to shew how that might be done, that we may know our friends some miles off, and read the smallest letters at a great distance, which can hardly be seen. A thing needful for mans use, and grounded upon the Opticks. And this may be done very easily; but the matter is not so to be published too easily; yet perspective will make it clear. Let the strongest sight be in the Centre of the Glass, where it shall be made, and all the Sun beams are most powerfully disperst, and unite not, but in the Centre of the foresaid Glass: in the middle of it, where diameters cross one the other, there is the concourse of them all. Thus is a Concave pillar-Glass made with sides equidistant: but let it be fitted by those Sections to the side with one oblique Angle: but obtuse Angled Triangles, or right Angled Triangles must be cut here and there with cross lines, drawn from the Centre, and so will the spectacle be made that is profitable for that use I speak of.

CHAP. XII.

How we may see in a Chamber things that are not.

I Thought this an Artifice not to be despised: for we may in any Chamber, if a man look in, see those things which were never there; and there is no man so witty that will think he is mistaken: Wherefore to describe the matter, Let there be a Chamber whereinto no other light comes, unless by the door or window where the spectator looks in: let the whole window or part of it be of Glass, as we use to do to keep out the cold; but let one part be polished, that there may be a Lookingglass on both sides, whence the spectator must look in; for the rest do nothing. Let Pictures be set over against this window, Marble statues, and such-like; for what is without will seem to be within, and what is behind the spectators back, he will think to be in the middle of the House, as far from the Glass inward, as they stand from it outwardly, and so clearly and certainly, that he will think he sees nothing but truth. But lest the skill should be known, let the part be made so where the Ornament is, that the spectator may not see it, as above his head, that a pavement may come between above his head: and if an ingenious man do this, it is impossible that he should suppose that he is deceived.

CHAP. XIII.

Of the operations of a Crystal Pillar.

NOr shall the operations of a Crystal Pillar go unspoken of, for in it there are some speculations not to be despised. First,

To kindle fire with a Crystal Pillar,

by opposing it to the Sun, it will kindle fire behind it about the circumference: ofttimes left above the Chamber, when the Sun shined, it burnt the Blankets. They that will at set hours and places burn the enemies camps, if it be laid upon fuel for fire, it will certainly kindle it. We may also

With a Crystal Pillar, make an Image hang in the Aire.

It will shew the Image hanging in the Air, both before and behind. Let the Object be behind the Pillar, let the Pillar be between that and the eye, the Image will appear outwardly hanging in the Air, above the Pillar, parted every where from the Pillar, clearly and perspicuously; and if the visible Object be between the eye and the Pillar, the Image will appear behind the Pillar, as I said. If it be a very visible Object, as fire or a candle, the matter is seen more clearly without any difficulty: I gave the reasons in my Opticks. We may also

In a Crystal Pillar see many Rain-bows.

Make a solid-Pillar in a Glass furnace, so great as a Walnut, and let it be made round onely by the fire, as the manner is, as Glass-makers use to do, that without any help of the wheel, the outward superficies may be most polite: where the Iron touched it, there leave a Pedestall. It is no matter for pure Glass, for impure is best: place this upon your eye, and a burning candle over against it; the light refracted by bladders will shew infinite Rain-bows, and all the light will seem Golden-colour'd, that nothing can be more pleasant to behold.

CHAP. XIV.

Of Burning-Glasses.

I Proceed to Burning-Glasses, which being opposed against the Sun beams, will kindle fire upon matter laid under them; In these also are the greatest secrets of Nature known. I shall describe what is found out by E[…]clide, Ptolomy, and Archimedes; and I shall add our own inventions, that the Readers may judge how far new inventions exceed the old. Fire is kindled by reflection, retraction, and by a simple and a compound Glass. I shall begin from a simple reflection, and from

A Concave-Glass that shall kindle fire behind it:

which few have observed. Know, that a Concave-glass will burn from its middle point, unto the hexagonal-side above the Glass, as far as a fourth part of its diameter;

[Figure]

from the hexagonal-side, as far as the tetragonal without the Glass, on the lower part of it: Wherefore cut off that part of the semicircle, which is situate from a pentagon as far as a tetragon, as it were the band of the circle; and this being polished, and opposed against the Sun, will cast fire far from it, behinde it. I will say no more, because I said more at large in my Opticks concerning this. So also we may

With a Concave Pillar or Pyramidal, kindle fire:

but very slowly, with delay onely, and in the Summer-Sun; it kindles in the whole line, and not in a point, but being extended by the point of accension of its circle. The same will fall out by a Pyramidal Concave.

CHAP. XV.

Of a Parabolical Section, that is of all Glasses the most burning.

THat is called a Parabolical Section, that more forcibly farther off, and in shorter time, will set matter on fire, that is opposite to it: it will melt Lead and Tin: My friends related to me, that Gold and Silver also; but I have made them red hot. By which invention of Archimedes, as appears by the testimony of Galen, and many more, We read that he set the Roman Navy on fire, when Marcellus besieged Syracuse, his Country. Plutarch in the life of Pompilius saith, The fire that burnt in Diana's Temple, was lighted by this Glass, that is, by instruments that are made of the side of right triangle, whose feet are equal: These made hollow, do from the circumference respect one Centre. When therefore they are held against the Sun, so that the beams kindled may be gathered from all parts, and be united in the Centre, and that they do fever the Air rarified, it soon sets on fire all fuel that is combustible opposed against it, by kindling first the lightest and driest parts; the beams being as so many fiery darts falling upon the Object. In a Concave spherical Glass the beams meeting together, kindle fire in a fourth part of the diameter under the Centre, which are directed within the side of a Hexagon from the superficies of the circle. But a Parabolical Section, is, wherein all the beams meet in one point from all the parts of its superficies. Cardanus teacheth how such a Glass should be made. If we would kindle fire at a mile distance, we must describe a circle, whose diameter must be two miles long; and of this we must take such a part, that the roundness of it may not lye hid, namely, a sixtieth part, to which we must add a dimetient, according to the altitude in one point, and upon the fixt diameter must we bring about part of the circle, which shall describe the portion of a Sphere; which when we have polished, if we hold it against the Sun, it will kindle a most violent fire a mile off. 'Tis strange how many follies he betrays himself guilty of, in these words. First, he promiseth a Glass should burn a mile off; which I think is impossible to burn thirty foot off, for it would be of a wonderful vastness; for the superficies of the Cane is so plain, & to receive any crookedness, it can hardly be made so great. Moreover, to describe a circle, whose diameter should be two miles long, what compasses must we use, and what plate shall we make it on, or who shall draw it about? And if it be true, that Archimedes by a Parabolical Glass did burn ships from the wall, the distance could not be above ten paces, as appears by the words of the Authors themselves; for in the same place he raised ships, and threw them against the Rocks: and his engines were Iron bars, the greatest part whereof lay backward; and by reason of those iron crows, it is manifest it could be done no other ways. There are other fooleries, but I pass them for brevity sake, that I might not seem tedious: the cause of his error was, that he never had made any such Glasses; for had he tried it, he would have spoke otherwise. But I will now shew how

To make a Glass out of a Parabolical Section.

The way to describe it is this: Let the distance be known how far we would have the Glass to burn, namely, AB ten foot; for were it more, it could hardly be done: double the line AB, and make ABC, the whole line will be AC: from the point A, draw a right line DA, and let DA and AE be equal one to the other, and cut at right Angles by AC, but both of them must be joined to the quantity AC, as DCE, which in C make a right Angle, DCE. Therefore the Triangle DCE is a right angled Triangle, and equal sides: and were this turned about the Axis CD, until it come to its own place whence it parted, there would be made a right angled Cane, EDNC, whose Parabolical Section will be ABC: the right line DC will be the Axis of the Cane, and CE shall be the semidiameter of the basis of the Cane: Through the point C you must draw a line parallel to DE, and that is HI of the length of CE and CD; and by the point B draw another parallel to the said line ED, which is FBG; and let BG and BF be both of them equal to AC: so FG shall be the upright side, and HI the basis of the Parabolical Section: If therefore a line be drawn through the points HEAGI, that shall be a Parabolical Section,

[Figure]

the Diagram whereof is this that follows. But if you will burn any thing, you must not make your Parabolical Glass to the bigness of the whole line HFAGI, but onely take a part thereof, as if we would take the top part of it LAM, that the line LM may cut AC in K, or greater or lesser: if you will make one greater, cut off AK beneath it; for the bigger it is, the more quickly and vehemently wil it burn; if you will have it less, take it above AK. But thus you must do, that the crooked line LAM may be more exactly described, that you may not commit the least error. Wherefore on a plain Table I protract the line ABC, and let AB be double the distance, that we intend to burn any thing, that is, the length of the line ABC: from the point B, I raise a perpendicular line BD, the altitude whereof must be of the same semidiameter of the Section to be made, that is the line LM, the half whereof is LK; from thence describe a semicircle, whose beginning A must pass through the point D. But you shall find the Centre thus: Let the points AD be joyned by a line, and let the Angle BAD be made equal to ADE, and the line DE drawn forth, shall cut AC in F, that shall be the Centre: so draw the semicircle ADC. If therefore we shall cut the line BC into smaller parts, so much the lesser Parabolical line must be described. Divide it into four parts, and let the points of the divisions be HGF: then describe three circles, that shall be termined by A from the three points HGF: the first is AF, the second AG, the third AH: and they shall cut

[Figure]

[Figure]

line BD; the first in F, the second in G, the thir[…] in H; thence I take my Section to be perfected LKM, and I cut the line KA into four parts, and thorow those points I draw parallel lines to LM. Let BH be the neerest to the top of the Parabolical Section, the second BG that follows next, and the third BF next to that, and after shall be LM. Thence by the lines LFGHA, draw a crooked line, and do the same on the other part so far as M, and that shall be the line sought for, to make the Parabolical Section, and from that must be made the Glass, as I shall shew.

CHAP. XVI.

How a Parabolical Section may be described, that may burn obliquely, and at a very great distance.

I Have described a Parabolical Section, which might be made by rule and compass, because we may use it at a short distance; but in greater distance we must proceed by numbers: as for forty or for sixty foot, and not much more, lest the Glass should be made of an unusual magnitude. The foresaid Glass burns between it and the Sun; and if the Sun be not as you desire it, the operation is lost: so also by an oblique Glass, that is between the Sun and the combustible matter, or over against it. Whence according to the situation you may use them all, namely, wherein they answer your expectation; and especially when the Sun is in the Meridian, they burn with more vehemency. This I must tell you, that you may not be deceived; for when you erre, you commonly draw others into error with you. A Parabolical Glass made from the top, if the Section shall be from the top, if we would burn far, the Glass will be plain; and that it may have some crookedness, it will be wonderful great. And if the Section be about the basis, that will be worst of all; for from the least distance, it will be almost flat: wherefore that we may have it with some crookedness, we must take a line about the neck of the Section, not the head, nor the feet. Wherefore being to make a Glass of a Parabolical Section, about the neck of the Section, where the greatest crookedness of the Parabolical Section is made, and that may burn far from its superficies, to twenty foot distance; Let the line AB be the sinus versus eighteen foot long: from the point A, I raise a line to right Angles with AB, which shall be the line by which, the fourth part whereof is AB: cut AB in C, and let it be two foot, and CB sixteen foot: I multiply twice seventy two, and that makes one hundred forty and four; the square root of this is twelve; wherefore the line erected perpendicularly from the point C, unto the circumference of the Parabolical Section, will be DI of twelve foot, wherefore CI will be the line appointed: joyn

[Figure]

IB, and the Radius that must burn, will be in the point B that was sought for: Wherefore the ray of the Sun, that is equidistant to the sinus versus HI, is reflected by IB in B; the Latitude whereof will be about twenty foot: for the line IC of twelve foot, multiplied into it self, will make one hundred forty and four; and CB is sixteen foot, which multiplied into it self, makes two hundred fifty and six; adde these together, and they make four hundred: the square root of it is twenty foot, thus. Wherefore I am resolved to take the part of the Glass, intercepted between the points I and F, and I seek two thirds of one foot, from C toward B, and I divide one foot into thirty parts, that the crookedness may be taken more precisely; and let CG be twenty parts of a foot, from A to C sixty parts, because they are two foot: wherefore from A to G, where we shall make our Glass, will be eighty parts. Wherefore let us begin from AC sixty parts, to which I always add four cyfers 0000. for this purpose, that when numbers come forth, whose roots cannot be extracted, those that are taken may be to the least loss: wherefore we shall make the Table under written. In the first line are the points of the sinus versus: in the second, the sqares, the lines to which; from the multiplication of the sinus versus, namely, the length AE, is seventy two foot: if we shall reduce these to parts, by multiplying by thirty, there comes forth 2160: multiply by the parts of the sinus versus AC, there will arise 129600: in the third line are roots of the foresaid number, namely, the lines appointed: adding therefore to 129600, four cyfers, they make 1296000000: the square root of this is 36000, of which last cyfers, one signifies the tenth part of a foot, another the tenth of a tenth part: thus, 360. 0. 0. 0. so will be the foresaid Table made.

[Figure]

These things being done, I take the differences of the roots, of the greatest to the smallest, for they are from 160. 0. 0. to 415. 6. 9. Make choice of the measure of a foot, according to which distances we would make our Glass: let it be AB, which we divide into thirty parts; and take twenty parts, namely, two thirds: I adde a line to it at right Angles, namely B, and let it be BC, which I divide into fifty five parts. I divide one part into ten, and that one into ten parts more, and those are tens of tens. Let A be nul, that is a cyfer, and there place sixty; the second part sixty one: the line joyned to right Angles, will be two; the third part sixty two; the line joyned to it will be five: so the twentieth part will be eighty, and the line joyned to the Angle fifty six: to the extremities of these lines I fasten a pin, and I put a brass Cithern-wire upon them, and upon it I draw a line, and the Parabolical line is exactly described by it; for should we draw it without the help of this cord, it will be wavering, and not perfect. Then take a brass Table of convenient thickness, and draw the line now found upon it, filing away all that that shall be above the line CA. These things being done, take an iron rod of an exact length, namely, twelve foot, as the line DC, and at the end fasten a plate, which shall be for the circumvolution of the axis; at the other end fasten a spike, that it may be fastned somewhere, and be handsomely turned about. So being well fixed, we turn it about, by adding clay mingled with straw, that it may excellent

[Figure]

well make a hollow place, like to the form of a Parabolical Section; which being dried, we must make another solid one, that it may contain the liquid Metal, as the maner is.

CHAP. XVII.

A Parabolical Section that may burn to infinite distance.

ZOnaras the Greek, writes in the third Tome of his Histories, That Anastasius moved sedition against Vitalianus a Thracian, and he got those of Mysia, and the Scythians to stand with him; and in the Country by Constantinople, he plundered the people, and besieged the City with a Fleet. Marianus the Deputy opposed him; and there being a fight at sea, by an engine made by Proclus a most excellent man, for he then was famous for Philosophy and Mathematicks; for he not onely knew all the secrets of the most eminent Artificer, Archimedes, but he found out some new inventions himself; the enemies Navy was vanquished. For Proclus is reported to have made Burning-Glasses of brass, and to have hanged them on the wall against the enemies Ships; and when the Sun beams fell upon them, that fire brake forth of them like to lightning, and so burnt their Ships and men at sea, as Dion reports that Archimedes did formerly to the Romans besieging Syracuse. But I will shew you a far more excellent way than the rest, and that no man as ever I knew writ of, and it exceeds the invention of all the Antients, and of our Age also; and I think the wit of man cannot go beyond it. This Glass doth not burn for ten, twenty, a hundred, or a thousand paces, or to a set distance, but at infinite distance: nor doth it kindle in the Cane where the rays meet, but the burning line proceeds from the Centre of the Glass of any Longitude, and it burns all it meets with in the way. Moreover, it burns behind, before, and of all sides. Yet I think it an unworthy act to divulge it to the ignorant common people: yet let it go into the light, that the immense goodness of our great God may be praised, and adored. Because a proportional Radius doth proceed from the greater Section, from the less is made the greater: to avoid this, make it of a Cylindrical Section, for it is the mean, and let it be set for the axis of the small and of the greater dissection, which may pass through the middle parallels: this held against the Sun, doth make refraction of the beams sent into it, very far, and perpendicularly from the Centre of a Cylindrical Section; and in this Art the reason cannot be found, that the beams uniting should part again: Wherefore it receives them directly, which it sends back again obliquely into beams far from the superficies of it. For the beams passing through the narrow hole of a window, are forthwith dilated; nor is their proportion kept, by being far removed, therefore it may reverberate and burn where the Cane seems clearest, which will be neer the Centre, nor is it far distant from the point where the rays meet; but neer the ray coming forth from that point, from the superficies of the Glass, called Parabolicall, which must remain firm in that place which I said before. Let experiment be made of its vertue, by threds passing from its Centre, or iron wire, or hair; and it is no matter whether it be Parabolical or Sphaerical, or any Section of the same order: then let it be excellent well fitted upon the Centre of the said Section: If the rays go forth above, or a little beneath, it is no matter, if not much money, or much money be laid out to make it. The making of it depends meerly on the Artificers hand; the quantity is nothing, be it small or great. The Latitude of the hollow is not necessary, onely let it be sent forth from the middle, that the rays may meet excellent well in the Centre. Let the window be made open aslaunt, that it may receive a Parabolical Glass; and thus shall you have a Glass, if that be well done I spake of. He that hath ears to hear, let him hear; I have not spoken barbarously, nor could I speak more briefly, or more plainly. But if a small one do not answer a great one in proportion, know that you will operate nothing: let it be large about the basis, small at the top, equidistant to the first. Let it not be a steel Glass, because it cannot sustain the heat of the burning, and by burning it loseth its brightness. Let it be therefore of Glass a finger thick: Let the Tin foil be of purged Antimony, and Lead, such as they make in Germany: let the form be of clay: put the Glass upon it, and melt it in a Glass furnace, that it may

[Figure]

take its form. This is a wonder, that that which causeth so much burning in the work, is cold, or at most but luke-warm. If you would have it burn before, of the Section which is about the basis, make a circle, in the middle point whereof fit the Artifice, that the ray returning, may come forth to the fore part. This I have said; and I have observed, that we may use this Artifice in great and wonderful things, and chiefly by inscribing letters in a full Moon. For whatsoever we have written by this Glass, as I said of a plain Glass, we may send letters of it to a very great distance: and because I said it sends forth to infinite distance, it is sent as far as the Moon, especially being helped by its light.