THE SEVENTEENTH BOOK OF Natural Magick: Wherein are propounded Burning-glass, and the wonderful sights to be seen by them.
NOw I am come to Mathematical Sciences, and this place requires that I shew some ex∣periments concerning Catoptrick-glasses. For these shine amongst Geometrical instru∣ments, for Ingen•ity, Wonder, and Profit: For what could be invented more ingeniously, then that certain experiments should follow the imaginary conceits of the mind, and the truth of Mathematical Demonstrations should be made good by Ocular experiments? what could seem more wonderful, then that by reciprocal strokes of reflexion, Images should appear out∣wardly, hanging in the Air, and yet neither the visible Object nor the Glass seen? that they may seem not to be the repercussion of the Glasses, but Spirits of vain Phantasms? to see burning Glasses, not to burn alone where the beams unite, but at a great distance to cast forth terrible fires, and flames, that are most profitable in warlike expeditions, as in many o∣ther things. We read that Archimedes at Syracuse with burning Glasses defeated the forces of the Romans: and that King Ptolomey built a Tower in Pharos, where he set a Glass, that he could for six hundred miles, see by it the enemies Ships, that invaded his Country, and plundered it. I shall adde also those Spectacles, whereby poor blinde people can at great distance, perfectly see all things. And though venerable Antiquity seem to have invented many and great things, yet I shall set down greater, more Noble, and more Famous things, and that will not a little help to the Optick Science, that more sublime wits may increase it infinitely. Lastly, I shall shew how to make Crystal and Metal Glasses, and how to polish them.
Divers representations made by plain Glasses.
I Shall begin with plain Glasses, for they are more simple, and the speculations thereof, are not so laborious, though the ap∣paritions of them be almost common, yet they will be useful for what follows: and we shall add some secret apparitions unto them. The variety of the Images that appear, proceed either from the matter or form of the Glass. Crystal must be clear, transparent, and exactly made plain on both sides: and if one or both of these be wanting, they will represent divers and deformed apparitions to our sight. I shall therefore begin from the matter, and shew
How apparitions may seem to him that looks upon them, to be pale, yellow, or of divers colours.
When the Glass is melted with heat in the furnace, with any little colour it will be tainted; if you cast in yellow, the face of him that looks into it, will seem to have they yellow Jaundies; if black, he will appear wan and deformed; if you add much of it, like to a blackmoore; if red, like a drunkard or furious fellow; and so will it re∣present Page 356 Images of any colour. How to mingle the colours, I taught when I spake of Jewels. I have oft made sport with the most fair women, with these Glasses; when they looked, and saw not themselves as they were: but there are many varieities a∣rise from the form.
That the face of him that looks on the Glass may seem to be divided in the middle,
Let the superficies of the looking-glasse that you look on, be plain, and exactly polished by rule; but the backside must have a blunt angle in the middle, that the highest part of it may be in the middle; in the outward parts it must be sharp and pressed down; then lay on the foil: wherefore the Image that falls on your sight, where the lines meet in the angle, will seem divided into two. If you will
That he that looks in the Glass, shall seem like an Ass, Dog, or Sow;
By variation of the place, the Angles, and the representation of the Form beheld, will seem various. If that part of the Glass, that is set against your mouth, shall stick forth before like a wreathed band or a Boss-buckler, your mouth will appear to come forth like an Asses or Sows snout; but if it swell forth against your eyes, your eyes will seem to be put forth like shrimps eyes; if the Angle be stretched forth by the length of the Glass, your Forehead, Nose, and Chin, will seem to be sharp, as the mouth of a Dog.
That the whole face may seem various and deformed.
Let a plain Glass not be exactly plain and even: which that it may be done, when the Glass is once made plain, put it into the furnace again, and let it be turned by the skilful hand of an Artist, till it lose its right position, then foil it. Then the Image on the hollow part of the Glass, will represent the opposite part hollow; so it will hold forth one lying along on his face, or crooked, and swelling outwardly and in∣wardly. Then if when the Glass is polished, one side be rubbed, the face will seem long and broad: wherefore it must be rubbed, and fashioned on all sides, that it may every way represent a perfect face. I shall shew you also
How to make a Glass to represent many Images.
That it may shew divers Images one after another, and of divers colours, make the solid body of the Looking-glass, or Glass that is half a finger thick, and let it be so plained, that upon one side, the thickness may not be touched, but on the other side, the lines of the two superficies may meet, as the sharp edge of a Knife. M•ke also another table of a Glass the same way: or else more; lay a foil of Tin upon the last, and place one of them upon the other, so that the thinner part of the one, may lye upon the thick part of the other: so will the face of one that looks into it, appear to be two, one behind the other, and the nethermost will always appear darkest. So if by the same Artifice, you fit three tables of Glass, the Image will appear to be three, and the farther he that looks, stands with his face from the Glass, the farther will those Images or faces stand asunder; but as you come very neer, they seem to joyn all in one: If you hold a Candle lighted against it, there will be many seen together, which comes by the mutual reciprocation of the sight and the Glasse▪ and if the po∣lishers of Glasses be not neer-hand, we may make the same with common Looking-glasses, putting one aptly above another, but let one be distant from the other by certain courses; then shut them in a frame, that the Art may not be discovered. Nor will I omit
How letters may be cast out and read, on a wall that is far distant;
which we shall do with the same plain Glass; and lovers that are far asunder, may so hold commerce one with another. On the superficies of a plain Glass, make Let∣ters with black ink, or with wax, that they may be solid to hinder the light of the Glass, and shadow it; then hold the Glass against the Sun-beams, so that the beams re∣flecting on the Glass, may be cast upon the opposite wall of a Chamber, it is no doubt but the light and letters will be seen in the Chamber, the Suns light will be Page 357 clearest, and the letters not so bright; so that they will be clearly discovered, as they are sent in.
Other merry sports with plain Looking-glasses.
NOw I shall annex some other operations of a plain Glass, described by our Ance∣stors, that I may seem to leave out nothing: and I will so augment them, and bring them to a rule, that they may be easily made. I shall begin with this,
How by plain Looking-glasses, the head may appear to be downwards, and the heels upwards.
If any man by plain Glasses, desires to see his head downward, and his feet upward (though it is proper for Concave-Glasses to represent that) yet I will endeavour to do it by plain Glasses. Place two Glasses long-ways, that they may stick together, and cannot easily come asunder, or move here and there, and that they make a right Angle; when this is so done, according to coherence the long way, set this against your face, that in one, half the face, in the other the other half may be seen; then incline the Looking-glasse to the right or left hand, looking right into it, and your head will seem to be turned, for according to their latitude, they will cut the face into two, and the Image will appear so, as if the head were under, and the heels upwards; and if the Glass be large, the whole body will seem to be inverted. But this happens from the mutual and manifold reflection, for it flies from one to the other, that it seems to be turned. We may
Make a plain Glass that shall represent the Image manifold.
A Glass is made that will make many representations, that is, that many things may be seen at once; for by opening and shutting it, you shall see twenty fingers for one, and more. You shall make it thus: Raise two brass Looking-glasses, or of Crystal, at right Angles upon the same basis, and let them be in a proportion called sesqui∣altera, that is, one and half, or some other proportion, and let them be joyned together longways, that they may be shut and opened, like to a Book; and the An∣gles be divers, such as are made at Venice: For one face being objected, you shall see many in them both, and this by so much the straighter, as you put them together, and the Angles are less: but they will be diminished by opening them, and the Angles being more obtuse, you shall see the fewer: so shewing one figure, there will be more seen: and farther, the right parts will shew right, and the left to be the left, which is contrary to Looking-glasses; and this is done by mutual reflection and pul∣sation, whence ariseth the variety of Images interchangably. We may
Make a Glass of plain Glasses, wherein one Image coming, is seen going back in another.
Take two plain Glasses, the length whereof shall be double, or one and half to the latitude, and that for greater convenience: for the proportion is not material; but let them be of the same length, and equal, and laid on the top of a Pillar, incli∣ning one to the other, and so joyn'd together; and let them be set upright upon some plain place perpendicularly, so the Glasses fastned, may be moved on the move∣able side. It is no doubt but you shall see the Image to come in one, and go back in the other Glass; and the more this comes neer, the farther will the other go; and in one will it be seen coming, and in the other going. Also you may see
In plain Glasses those things that are done afar off, and in other places.
So may a man secretly see, and without suspition, what is done afar off, & in other pla∣ces, which otherwise cannot be done: but you must be careful in setting your Glasses. Let there be a place appointed in a house or elsewhere, where you may see any thing, and set a Glass right over against your window, or hole, that may be toward your face, and let it be set straight up if need were, or fastned to the wall, moving it here Page 358 and there, and inclining it till it reflect right against the place; which you shall at∣tain by looking on it, and coming toward it: and if it be difficult, you cannot mi∣stake, if you use a quadrant or some such instrument; and let it be set perpendicular upon a line, that cuts the Angle of reflection, and incidence of the lines, and you shall clearly see what is done in that place. So it will happen also in divers places. Hence it is, that if one Glass will not do it well, you may do the same by more Glas∣ses; or if the visible Object be lost by too great a distance, or taken away by walls or mountains coming between; moreover, you shall fit another Glass just against the former, upon a right line, which may divide the right Angle, or else it will not be done, and you shall see the place you desire. For one Glass sending the Image to the other tenfold, and the Image being broken by many things, flies from the eye, and you shall see what you first light upon, until such time as the Image is brought to you by right lines, and the visible Object is not stopt by the windings of places or walls: and the placing of it is easie. So oft-times I use to convey Images of things. But if otherwise you desire to see any high place, or that stands upright, and your eye cannot discern it; fit two Looking-glasses together long-ways, as I said, and fasten one upon the top of a post or wall, that it may stand above it, and the Object may stand right against it; the other to a cord, that you may move it handsomely when you please, and that it may make with the first sometimes a blunt, sometimes a sharp Angle, as need requires, until the line of the thing seen, may be refracted by the mid∣dle of the second Glass to your sight, and the Angles of reflection and incidence be equal; and if you seek to see high things, raise it; if low things, pull it down, till it beat back upon your sight, then shall you behold it. If you hold one of them in your hand, and look upon that, it will be more easily done. I shew you also
How to make a Glass that shall shew nothing but what you will.
Also a Glass is so framed, that when you look into it, you shall not see your own pi∣cture, but some otherface, that is not seen any where round about. Fasten a plain Glass on a wall upon a plain, set upright perpendicularly, and bow the top of it to the known proportion of the Angle: right against it cut the wall, according as the pro∣portion of some Picture or Image may require, and set it by it, according to a fit distance, and cover it, that the beholder may not see it (and the matter will be the more wonderful) nor can come at it: The Glass at a set place will beat back the Image, that there will be a mutual glance of the visible Object and the sight, by the Looking-glasses: there place your eye; you shall find that place, as I taught you be∣fore. Wherefore the spectator going thither, shall neither see his own face, nor any thing else besides: when he is opposed to it, and comes to the set place, he shall see the Image or the Picture, or some such thing, which he can behold nowhere else. You shall now know
How a Glass may be made of plain Glasses, whereby you may see an Image flying in the Air.
Nor is that Glass of less importance, or pleasure, that will represent men flying in the Air. If any man would do it, it is easily done thus: Fit two pieces of wood toge∣ther like a square or gnomon of a Dial, and being well fastned, they may make an Angle as of a right angled triangle, or Isosceles. Fasten then at each foot one great Looking-glass, equally distant, right one against the other, and equidistant from the Angle: let one of them lye flat, and let the spectator place himself about the middle of it, being somewhat raised above the ground, that he may the more easily see the form of the heel going and coming: for presently you shall perceive, if you set your self in a right line, that cuts that Angle, and it be equidistant to the horizon. So the representing Glass will send that Image to the other, which the spectator looks into, and it will shake and move the hands and feet, as Birds do when they fly. So shall he see his own Image flying in the other, that it will always move, so he de∣part not from the place of reflection, for that would spoil it.
A Looking-glass called a Theatrical Glass.
PRudent Antiquity found out a Looking-glass made of plain Glasses, wherein if one Object might be seen, it would represent more Images of the same thing; as we may perceive by some writings, that go in Ptolomies name. Lastly, I shall add to this what our age hath invented, that is far more admirable and pleasant. Wherefore
To make an Antient fashioned Looking-glass of plain Glasses, wherein more Pictures will be represented of the something.
The way is this; make a half circle on a plain Table, or place where you desire such a Glass to be set up; and divide this equally with points according to the number of the Images you would see. Make subtendent lines to them, and cut away the arches; then erect plain Looking-glasses, that may be of the same latitude, and of the same parallel lines, and the same longitude; glew them fast together, and fit them so, that they may not be pulled asunder, as they are joyned long-ways, and erected upon a plain superficies. Lastly, let the spectator place his eye in the cen∣tre of the circle, that he may have his sight uniform, in respect of them all; in each of them you shall see a several face, and so quite round, as we see it often when peo∣ple dance round, or in a Theatre, and therefore it is called a Theatrical Glass: For from the centre all the perpendicular lines fall upon the superficies, and they are re∣flected into themselves; so they reflect the Images upon the eye, each of them draw∣ing forth its own. This is the Antients way of making a Theatrical Glass; but it is childish: I will shew you one that is far more pleasant, and wonderful; for in the former, the Images were seen no more than the Glasses were in number; but in our Glass, by the manifold and reciprocal da•tings of the Object and the Glass, you may see far more, and almost infinite Images. The way is this.
How to make an Amphitheatrical-Glass.
Make a circle on a Table what largeness you desire, and divide it into unequal parts; and in the place where the Object or Face to be seen must be opposed, leave two void spaces: over against the parts, let a right line be made upon the lines that de∣termine the parts, let Looking-glasses be raised perpendicularly; for the face that shall be against the Looking-glass, placed in the middle, will fly back to the beholder of it, and so rebounding to another, and from that to another, and by many reflecti∣ons you shall see almost infinite faces, and the more the Glasses are, the more will be the faces: If you set a Candle against it, you shall see innumerable Candles. But if the Glasses you erect, shall be of those already described, from so many divers faces of Asses, Sows, Horses, Dogs; and of colours, yellow, Brown, red, the specta∣tors shall see a far more wonderful and pleasant sight, for by reason of the manifold reflection, and diversity of the forms of the Glasses, and colours, an excellent mix∣ture will arise.
Divers operations of Concave-Glasses.
BUt the operations of Concave-glasses are far more curious and admirable, and will afford us more commodities. But you can do nothing perfectly with it, until you know first the point of inversion. Therefore that you may do it the better, and more easily
Know the point of Inversion of Images in a Concave-glass,
Do thus: Hold your Glass against the Sun, and where you see the beams unite, know that to be the point of Inversion. If you cannot well perceive that, breathe a thick vapour from your mouth upon it, and you shall apparently see where the coincidence is of the reflected beams; or set under it a vessel of boyling water. When you have found the point of Inversion, if you will Page 361
That all things shall seem greater.
Set your head below that point, and you shall behold a huge Face like a monstrous Bacchus, and your finger as great as your arm: So women pull hairs off their eye∣brows, for they will shew as great as fingers. Seneca reports that Hostius made such Concave-Glasses, that they might make things shew greater: He was a great pro∣voker to lust; so ordering his Glasses, that when he was abused by Sodomy, he might see all the motions of the Sodomite behind him, and delight himself with a false re∣presentation of his privy parts that shewed so great.
To kindle fire with a Concave-Glass.
This Glass is excellent above others, for this, that it unites the beams so strongly, that it will shew forth a light Pyramis of its beams, as you hold it to the Sun; and if you put any combustible matter in the centre of it, it will presently kindle and flame, that with a little stay will melt Lead or Tin, and will make Gold or Iron red hot: and I have heard by some, that Gold and Silver have been melted by it; more slow∣ly in winter, but sooner in summer, because the medium is hotter; at noon rather than in the morning, or evening for the same reason.
To make an Image seem to hang in the Air, by a Concave-Glass.
This will be more wonderful with the segment of a circle, for it will appear farther from the Glass. If you be without the point of Inversion, you shall see your head downwards. That with fixed eyes, and not winking at all, you may behold the point, until it comes to your very sight: For where the Cathe•us shall cut the line of reflection, there the species reflected will seem almost parted from the Glass: the neerer you are to the Centre, the greater will it be, that you will think to touch it with your hands: and if it be a great Glass, you cannot but wonder; for if any man run at the Glass with a drawn sword, another man will seem to meet him, and to run through his hand. If you shew a Candle, you will think a Candle is pendu∣lous lighted in the Air. But if you will
That the Image of a Concave-Glass should go out far from the Centre;
when you have obtain'd the Image of the thing in its point, if you will have it farther distant from the Centre, and that the Picture of a thing shall be farther stretched forth, then you shall decline from the point a little toward the right or left hand, about the superficies of the Glass, and the Image will come forth the farther, and will come to your sight: There, namely where the Catherus doth the farthest off that is possible touch the line of reflection, which few have observed: from which principle many strange wonders may be done. When you have this, you may easily
Reflect heat, cold, and the voice too, by a Concave-Glass.
If a man put a Candle in a place, where the visible Object is to be set, the Candle will come to your very eyes, and will offend them with its heat and light. But this is more wonderful, that as heat, so cold, should be reflected: if you put snow in that place, if it come to the eye, because it is sensible, it will presently feel the cold. But there is a greater wonder yet in it; for it will not onely reverberate heat and cold, but the voice too, and make an Eccho; for the voice is more rightly re∣flected by a polite and smooth superficies of the Glass, and more compleatly than by any wall. I prove this, because, if a man turn his face to the Glass, and his friend stand far behind his back, when he beholds his face, he shall decline his face from the point of Inversion; but on the right hand, about the superficies of the Glass, and his face will come forth far from the Glass, and will seem very great about the face of his friend: Whatsoever he shall speak with a low voyce against the Glass, he shall hear the same words and motions of his mouth, and all motion from the mouth of the reflected Image; and they that stand in the middle between them, shall per∣ceive nothing at all. But he that would send his own Image to his friend, must ob∣serve till his head shall come to the Glass. It is profitable also Page 362
By a Concave-Glass to see in the night what is done afar off.
By this very Glass, we may in a tempestuous night, in the middle of the streets, cast the light a great way, even into other mens Chambers. Take the Glass in your hand, and set a Candle to the point of Inversion, for the parallel beams will be re∣flected to the place desired, and the place will be enlightned above sixty paces, and whatsoever falls between the parallels, will be clearly seen: the reason is, because the beams from the Centre to the circumference, are reflected parallel, when the parallels come to a point; and in the place thus illuminared, letters may be read, and all things done conveniently, that require great light. By the same Art we may
With a few small lights give light to a great Hall.
In Temples, Watches, and nightly Feasts, any man may thus with a few lights make a great light. At two or more places of the Chamber set Concave-glasses above, and let them be so ordered, that the place of concurrent parallels may be coinci∣dent in the place required; and in the point of Inversion of them, the light will be so multiplied, that it will be as light as noon-day. Lamps are best for this purpose, because the light varies not from the place. Candles are naught, because they alter the places of reflection. More commodiously then by a plain Glass, to signifie by a Concave-glass, secretly some notes to your friend: Thus, do as I said, make the marks upon your Glass superficies with wax or some dark substance, and setting it against the light, it will cast the light upon the walls of the Chamber, and there it will be dark where the letters are made: one that knows the craft, may easily read them. But this is more admirable for one that knows not the cause,
To read letters in a dark night.
A Concave-Glass is of great use for this, and it may be this may be good in time of necessity. Set your Concave-Glass against the Stars of the first magnitude, or a∣gainst Venus or Mercury, or against a fire or light that is afar off; for the light re∣flected will meet in the point of burning, and reflects a most bright light, whereby you may easily read the smallest letters; for putting the point of reflection to every word, you shall see all clearly. But this is more necessary and profitable,
At any hour of the day with a Concave-Glass, to set a House or Fort on fire.
You may so burn the enemies Ships, Gates, Bridges, and the like, without danger or suspicion, at a set hour of the day, appointed the day before. Set your Glass a∣gainst the Sun, and order it so, that the coincidence of the beams may fall upon the point: lay fuel there, and things that will take fire, as I shewed you: and if you would blow up Towers, make heaps of Gun-powder: at night set your Glass, and hide it, that it be not seen, for the next day the Sun will fall upon the same point, where you set fuel for the fire.
Of the mixt operations of the plain Concave-Glasses.
I Shall set down the mixt operations and benefits of both these Glasses, that what one cannot do alone, it may do by the help of another. If we would
Kindle fire afar off with a plain and a Concave-Glass.
It falls out sometimes that one shut up in prison needs fire, and the Sun beams shine not in: or else I will shew how we may kindle Gun-powder without fire, or make mines and fill them with Gun-powder, to blow up Castles or Rocks afar off without danger, setting them on fire by a plain Glass. A plain Glass as it receives the pa∣rallel beams of the Sun, it so reflects them, and therefore will cast the beams that are equidistant, a great way: but if a Concave-Glass receive them, it so unites them, that it sets things on fire. Wherefore, first proving where the Concave-Glass must be Page 363 placed, that it may fire the fuel cast in: the next day, at the hour appointed, let the plain Glass cast in the beams upon the Concave-glass, that will unite them: so with∣out danger, or any suspicion of the enemy, we may kindle fire for our use. Nor is it useless,
That by a plain and Concave-Glass the smallest letter shall appear very great,
when letters are so small that they can onely be seen: For I have seen St. Johns Go∣spel, In the beginning, &c. writ so small, in so little place, that it was no bigger than a small pimple, or the sight in a Cocks eye. By this Artifice we may make them seem greater, and read them with ease. Put a Concave-glass, with the back of it to your brest; over against it in the point of burning, set the writing: behind set a plain Glass, that you may see it: Then in the plain Glass will the Images of the Cha∣racters be reflected, that are in the Concave-glass, which the Concave-Glass hath made greater, that you may read them without difficulty. You may
With a plain and Concave-Glass, make an Image be seen hanging altogether in the Air.
Do thus. I said that by help of a Concave-Glass, an Image may be sent forth: and this is seen by none but those that stand over against it; Set the Concave-Glass to your brest, without the Centre place a Poniard against it, and going farther off, set a plain Glass against it; and looking in that, you shall see the Image reflected from the Concave-glass, hanging in the Air, and that exactly. But if an ingenious man observe it, he may wonderfully see an Image hanging in the Air, that is received in a plain Glass, and sent far out as I shewed, without the help of a Concave-glass, and a visible spectacle, by the means of a plain Glass onely. You may also
By a plain Glass see your face turned the wrong way.
When you have set the Glass to your brest, as I said; set a plain Glass against it, and look upon it, will cast it upon the Concave-glass, and that will beat it backwards on the plain Glass: so have you your purpose.
Other operations of a Concave-Glass.
BEfore I part from the operations of this Glass, I will tell you some use of it, that is very pleasant and admirable, whence great secrets of Nature may appear unto us. As,
To see all things in the dark, that are outwardly done in the Sun, with the colours of them.
You must shut all the Chamber windows, and it will do well to shut up all holes be∣sides, lest any light breaking in should spoil all. Onely make one hole, that shall be a hands breadth and length; above this fit a little leaden or brass Table, and glew it, so thick as a paper; open a round hole in the middle of it, as great as your little finger: over against this, let there be white walls of paper, or white clothes, so shall you see all that is done without in the Sun, and those that walk in the streets, like to Antipodes, and what is right will be the left, and all things changed; and the far∣ther they are off from the hole, the greater they will appear. If you bring your pa∣per, or white Table neerer, they will shew less and clearer; but you must stay a while, for the Images will not be seen presently: because a strong similitude doth some∣times make a great sensation with the sence, and brings in such an affection, that not onely when the senses do act, are they in the organs, and do trouble them, but when they have done acting, they will stay long in them: which may easily be perceived. For when men walk in the Sun, if they come into the dark, that affection continues, that we can see nothing, or very scantly; because the affection made by the light, is still in our eyes; and when that is gone by degrees, we see clearly in dark places. Now will I declare what I ever concealed till now, and thought to conceal continu∣ally. If you put a small centicular Crystal glass to the hole, you shall presently see Page 364 all things clearer, the countenances of men walking, the colours, Garments, and all things as if you stood hard by; you shall see them with so much pleasure, that those that see it can never enough admire it. But if you will
See all things greater and clearer,
Over against it set the Glass, not that which dissipates by dispersing, but which con∣gregates by uniting, both by coming to it, and going from it, till you know the true quantity of the Image, by a due appropinquation of the Centre; and so shall the be∣holder see more fitly Birds flying, the cloudy skies, or clear and blew, Mountains that are afar off; and in a small circle of paper (that is put over the hole) you shall see as it were an Epitomy of the whole world, and you will much rejoyce to see it: all things backwards, because they are neer to the Centre of the Glass, if you set them farther from the Centre, they will shew greater and upright, as they are, but not so clear. Hence you may,
If you cannot draw a Picture of a man or any things else, draw it by this means;
If you can but onely make the colours. This is an Art worth learning. Let the Sun beat upon the window, and there about the hole, let there be Pictures of men, that it may light upon them, but not upon the hole. Put a white paper against the hole, and you shall so long fit the men by the light, bringing them neer, or setting them further, until the Sun cast a perfect representation upon the Table against it: one that is skill'd in painting, must lay on colours where they are in the Table, and shall describe the manner of the countenance; so the Image being removed, the Picture will remain on the Table, and in the superficies it will be seen as an Image in Glass. If you will
That all shall appear right,
This is a great secret: many have tryed it, but none could obtain it: For some setting Plain Glasses obliquely against the hole, by reverberation against the Table, they could see some things somewhat direct, but dark and not discernable. I oft-times by putting a white paper obliquely against the hole, and looking just against the hole, could see some things direct: but a Pyramis cut obliquely, did shew men with∣out proportion, and very darkly. But thus you may obtain your desire: Put a∣gainst the hole a convex Glass; from thence let the Image reflect on a Concave∣glass: let the Concave-glass be distant from the Centre, for it will make those I∣mages right, that it receives turned, by reason of the distance of the Centre. So up∣on the hole and the white paper, it will cast the Images of the Objects so clearly and plainly, that you will not wonder a little. But this I thought fit to let you under∣stand, lest you fail in the work, that the Convex and Concave-glasses be proporti∣onable circles: how you shall do this, will be here declared often. I shall shew also,
How in a Chamber you may see Hunting, Battles of Enemies, and other delusions.
Now for a conclusion I will add that, then which nothing can be more pleasant for great men, and Scholars, and ingenious persons to behold; That in a dark Chamber by white sheets objected, one may see as clearly and perspicuously, as if they were before his eyes, Huntings, Banquets, Armies of Enemies, Plays, and all things else that one desireth. Let there be over against that Chamber, where you desire to represent these things, some spacious Plain, where the Sun can freely shine: Upon that you shall set Trees in Order, also Woods, Mountains, Rivers, and Animals, that are really so, or made by Art, of Wood, or some other matter. You must frame little children in them, as we use to bring them in when Comedies are Acted: and you must counterfeit Stags, Bores, Rhinocerets, Elephants, Lions, and what other creatures you please: Then by degrees they must appear, as coming out of their dens, upon the Plain: The Hunter he must come with his hunting Pole, Nets, Arrows, and other necessaries, that may represent hunting: Let there be Horns, Cornets, Trumpets sounded: those that are in the Chamber shall see Trees, Animals, Hun∣ters Faces, and all the rest so plainly, that they cannot tell whether they be true Page 365 or delusions: Swords drawn will glister in at the hole, that they will make people almost afraid. I have often shewed this kind of Spectacle to my friends, who much admired it, and took pleasure to see such a deceit; and I could hardly by natural reasons, and reasons from the Opticks remove them from their opinion, when I had discovered the secret. Hence it may appear to Philosophers, and those that study Opticks, how vision is made; and the question of intromission is taken away, that was antiently so discussed; nor can there be any better way to demonstrate both, than this. The Image is let in by the pupil, as by the hole of a window; and that part of the Sphere, that is set in the middle of the eye, stands in stead of a Crystal Table. I know ingenious people will be much delighted in this. It is declared more at large in our Opticks. From hence may one take his principles of declaring any thing to one that is confederate with him, that is secret, though the party be far off, shut up in prison. And no small Arts may be found out. You shall amend the distance by the magnitude of the Glass. You have sufficient. Others that under took to teach this, have utter'd nothing but toyes, and I think none before knew it. If you desire to know
How you may see the Sun Eclipsed,
Now I have determined to shew how the Suns Eclipse may be seen. When the Sun is Eclipsed, shut your Chamber-windows, and put a paper before a hole, and you shall see the Sun: let it fall upon the paper opposite from a Concave-glass, and make a circle of the same magnitude: do so at the beginning, middle, and end of it. Thus may you without any hurt to your eyes, observe the points of the diameter of the Suns Eclipse.
How you may see in the dark▪ what is light without by reason of Torches.
VVE may demonstrate the same without the light of the Sun, not without won∣der. Torches, or lights lighted on purpose in Chambers, we may see in another dark Chamber what is done, by fitting things as I said: but the light must not strike upon the hole, for it will hinder the operation; for it is a second light that carries the Images. I will not conceal at last a thing that is full of wonder and mirth, because I am faln upon this discourse,
That by night an Image may seem to hang in a Chamber.
In a tempestuous night the Image of any thing may be represented hanging in the middle of the Chamber, that will terrifie the beholders. Fit the Image before the hole, that you desire to make to seem hanging in the Air in another Chamber that is dark; let there be many Torches lighted round about. In the middle of the dark Chamber, place a white sheet, or some solid thing, that may receive the Image sent in: for the spectators that see not the sheet, will see the Image hanging in the mid∣dle of the Air, very clear, not without fear and terror, especially if the Artificer be ingenious.
How without a Glass or representation of any other thing, an Image may seem to hang in the Air.
BEfore I part from this Image hanging in the Air, I will shew how you may make the Images of all things seem to hang in the Air, which will be a wonder of wonders; chiefly being done without the apparition of a Glass, or a visible Object. But first we will examine what the Antients writ of this matter. One Vitellio de∣scribes the business after his fashion, thus: Fasten the segment of a Cylinder in the middle of the house, set upon a Table, or Stool, that it may glance perpendicularly Page 366 upon the ground; then place your eye at some hole or chink that is somewhat di∣stant from the Glass, and let it be fixed, that it may not move here and there: over against the Glass break the wall, and make it like to a window: let it be Pyramidal in shape, and let the sharp point be within, and the basis without, as men use to do, when a Picture or any Image is placed for the eye to look upon; but let it be reflected on by the superficies of the Pyramidal Glass, that the Picture placed with∣out, which your eye cannot see through the hole, may seem to hang pendulous in the Air; which will cause admiration to behold. A Pyramidal Convex-glass will do the same, if you fit it so that it may represent the same Image. It may be done also by a Sphaerical Convex and Concave. But the matter promiseth more in the Frontispiece written upon it, then it will performe in the conclusion. Wherefore the Image will be seen without the Glass, but by the means of the Glass; so that the thing beheld in the Glass, will seem to be without it. But he is foully mistaken here, as in other places. He had said better, by a Cylinder of Crystal: For as a pillar it would make an irradiation outwardly, yet it would be worse seen than in the pillar, as I shall shew. But I shall discover what I purposed always to conceal;
That neither the Object nor Glass may be seen, yet the Image shall seem to hang alone, pen∣dulous in the middle of the Chamber;
And walking about, you shall behold the Image every where. But is such a thing fit to be discovered to the people? shall I do such an unworthy Act? Ah! my pen falls out of my hand. Yet my desire to help posterity, overcomes; for perhaps from this gleaning as it were, greater and more admirable inventions may be produced. Let it be so: get not a Sphaerical Cylinder, or Convex diflection of a Pyramidal Concave, the portion of which segment is not known; but let it be that which may descend upon his right Angle by a half Cylinder and a square, and is parted by an oblique Angle. Of two parts it must be received pendulous, and beneath in the half of its diameter it is conveyed from the middle. Let all the windows of the house be shut: stop all the chinks, that the light may not come in beneath. In that place where the spectacle is prepared, if the Sun or Moon beams fall in, the whole shew is spoiled. So place the beams of the Image that are beaten back, that the head of it may by repercussion fall right upon the earth. So will the visible Object that comes by reper•ussion, be reflected above and beneath; It will follow the fashion of the first Glass: let a Brass or Marble Table be so placed upon it, as we said; and lest the light falling from the window should light upon the plain Cylinder, and the crooked Glass, it mu• be stopped by a shutter of a hands-breath, that is three times as broad as the hole; for it will break forth every way: You shall cover the appari∣tion, that the Image may be fitted very deep, that there may seem to be a pit: as the beams meet, let the spectator come, who cannot be in any great mistake. But cover your sight round, that the Glass offend not your eye. Then is the Image seen, and it shall not appear above the Table, where the falling of the Cathetus will cut the line of sight through the Centre of the Glass. I could open the matter no plainer, I have done what I could: I know he that can understand it, will rejoyce very much.
Mixtures of Glasses, and divers apparitions of Images.
NOw will I try to make a Glass, wherein many diversities of Images shall appear: and though such a one be hard to make, yet it will recompence all by the di∣versity of Images, and the benefit of it. If then you would
Make a Glass that shall represent much diversity of Images.
Take a great or small circle, as you would have your Glass, and here and there cut off two parts of the circumference, one to the quantity of a Pentagon, the other of a Hexagon, as is clear in the Mathematicks: let the arch of the Pentagon be made hollow with some table, or Iron, that it may exactly receive it into it, and may seem Page 367 to be cut out of it; but the side of the Hexagon shall be contrary to this, for the quanti∣ty of that must be received by a Convex Table, that the arch of it may so stick forth: Then take a foil of Wax or Lead, of a convenient thickness, that exceeds the breadth of the arch of the Hexagon, and in length exceeds them both: Then crook this plate so, that it may exactly stand in the hollow of the wood, that there be no space or chink left between them; then let the Convex superficies that is preserved pro∣minent, be applied inwardly, according to the breadth of it; that the form of the Concavity may not be against the Convexity, but that the same plate may receive both portions without impediment: Having thus made your model, make your Glass of steel, or of some other mixture, as I shall shew you; and when it is polished, it will shew you many diversites of Images. First, the right parts will shew right, and the left the left, whereas the nature of plain Glasses, is to shew the right side as left, and the left side as right: and if you go backwards, the Image will seem pro∣portionable, and will come forward: if you come more towards the Convex super∣ficies, the Image will shew ugly; and the neerer you come, the uglier will it shew, and be more like a hories head. If you incline the Glass, that will incline too; and by varying the Glass, and the situation of it, you shall perceive divers variations; sometimes the head down, and the heels up; and you shall see many other things that I think not needful to relate now: for being placed on a voluble set, that it may shew both parts before and behind, the spectator of himself may see all things. We may
Make a Glass out of all,
that in that alone all Images may be seen, that are seen in all: many mouths; some∣times greater, sometimes less, sometimes right, sometimes left, some neerer, some far∣ther off, some equidistant. If a crooked be set in one place, in another a Concave, and a plain one in the middle, you shall see great diversity of Images. These are
The operations of a Convex Cylindrical Glass.
When your face is against it, the more deformed it appears in length, the more ugly it is for slenderness: if the length of it cut the face overthwart, it shews a low pres∣sed down face like a Frogs, that you shall see nothing but the teeth: almost the same way, as you shall see it in a Sword, or any other long and polished steel: if you in∣cline it forward, the forehead will appear very great, the chin small and slender like a horse. But contrary to these are
The operations of Cylindrical Concave-glasses.
If you look into the Concave, you shall see more Images of the same thing, imitating the said Glass. If you set your eye to the Centre, you shall see it all the breadth of the Glass; so your forehead, mouth, and the rest. If you turn such a Glass, that it may cut your face broad-ways, you shall presently see your head inverted, and the rest that I related in the Concave-glass.
The operations of a Pyramidal Glass turned,
are these: You shall see a sharp forehead, and a large chin. But the contrary way, a long forehead, with a very long nose. In a Concave you shall behold many faces, if according to the concavity you fit many portions of plain Glasses: for one looking into it, shall find them as many as there are Glasses, and all moving a like; and again, what Glass soever it be, if it be not plain, it shall shew always different from the Image.
Of the effects of a Lenticular Crystal.
MAny are the operations of a Lenticular Crystal, and I think not fit to pass them over in silence. For they are Concaves and Convexes. The same ef∣fects are in spectacles, which are most necessary for the use of mans life; whereof no man yet hath assi•n'd the effects, nor yet the reasons of them. But of these more at large in our Opticks. That no space may be empty, I shall touch some things here; I call Lenticulars, portions of circles compacted together, of Concaves and Convexes. I will first shew
How with a Convex Crystal Lenticular to kindle fire.
A Convex Lenticular kindleth fire most violently, and sooner, and more forcibly then a Concave-glass: I gave the reasons in my Opticks. For being held against the Sun, when the beams meet in the opposite part, it will kindle fire it is opposite to, melt Lead, and fire Metals. Moreover, if you will
By night give light afar off with a Lenticular Crystal,
Set a Candle a little behind the point of burning, so it will cast parallels a very great way to the opposite part, that you may see men pass the streets, and all things done in Chambers that are far from you. The same way as I said of a Concave-glass, we may
In a dark night read a letter by a Lenticular Crystal:
Put the letter behind the Glass, against the Stars or Candles a great way from you; where the beams meet, the words that are opposite will be clearly seen in a dark night, and the Chamber shut. But that which follows, will afford you a principle far better for your consideration: Namely,
By a Lenticular Crystal to see things that are far off, as if they were close by.
For setting your eye in the Centre of it behind the Lenticular, you are to look upon a thing afar off, and it will shew so neer, that you will think you touch it with your hand: You shall see the clothes colours, mens faces, and know your friends a great way from you. It is the same
To read an Epistle a great way off with a Lenticular Crystal.
For if you set your eye in the same place, and the Epistle be at a just distance, the letters will seem so great, that you may read them perfectly. But if you incline the Lenticular to behold the Epistle obliquely, the letters will seem so great, that you may read them above twenty paces off. And if you know how to multiply Lenticu∣lers, I fear not but for a hundred paces you may see the smallest letters, that from one to another the Characters will be made greater: a weak sight must use spectacles fit for it. He that can fit this well, hath gain'd no small secret. We may
Do the same more perfectly with a Lenticular Crystal.
Concave Lenticulars will make one see most clearly things that are afar off; but Con∣vexes, things neer hand; so you may use them as your sight requires. With a Con∣cave you shall see small things afar off, very clearly; with a Convex, things neerer to be greater, but more obscurely: if you know how to fit them both together, you shall see both things afar off, and things neer hand, both greater and clearly. I have much helpe• some of my friends, who saw things afar off, weakly; and what was neer, confusedly, that they might see all things clearly. If you will, you may
By a Convex Lenticular Crystal see an Image hanging in the Air.
If you put the thing to be seen behind the Lenticular, that it may pass thorow the Cen∣tre, Page 369 and set your eyes in the opposite part, you shall see the Image between the Glass and your eyes; and if you set a paper against it, you shall see it clearly: so that a lighted Candle will seem to burn upon the Paper. But
By a Concave Lenticular to describe compendiously how long and broad things are.
A Painter may do it with great commodity, and proportion: for by opposition to a Concave Lenticular, those things that are in a great Plain are contracted into a small compass by it; so that a Painter that beholds it, may with little labour and skill, draw them all proportionably and exactly: but to leave nothing concerning specta∣cles, I will shew
How a thing may appear multiplied.
Amongst sports that are carried about, a spectacle is of no small account: that Glass Instrument we put to our eyes, to see the better with. For of those things that de∣lude the sight, there can be no better way invented, then by the medium; for that being changed, all things are changed. Wherefore prepare that of very solid thick Glass, that it may be the better worked by a wheel into proportions: wherefore fit it into many Forms and Angles, whereby we desire to multiply any thing: but in the middle of them, let the Angles be Pyramidal, and let it agree with the sight; that from divers Forms, Images may be retracted to the eyes, that they cannot discern the truth. Being now made of divers superficies, set them to your eyes; and if you look upon any mans face hard-by, you will think you see Argus, one that is all Eyes. If his nose, you shall see nothing but nose; so his hands, fingers, arms, that you shall see no man, but Briareus the Poet, faigned to have have an hundred hands. If you look upon Money, you shall see many for one, that you cannot touch it with your hands, but it will often deceive you; and it is better to pay with it then to receive. If you see a Galley afar off, you will think it is a fleet of war: If a Souldier walks, that it is an Army marching. And thus are things doubled, and men seem to have two faces, and two bodies, Thus are there divers ways to see, that one thing may seem to be another: and all these things will be evident to those that seek and enquire after them by tryal.
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 perspe∣ctive 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 ob∣lique 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.
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 Looking∣glass 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.
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: oft∣times 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 ap∣pear 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 no∣thing can be more pleasant to behold.
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 Ar∣chimedes; 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 diame∣ter;
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.
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 short∣er 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 cir∣cumference 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 combu∣stible 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 diame∣ter 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 po∣lished, Page 372 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 pro∣miseth 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 de∣scribe 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 other∣wise. 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 an∣gled 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,
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. Where∣fore 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 ere∣cted 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
|The points of sinus versus.||Multiplication of sinus versus with the line to which.||The square root.||Tenth parts.||Tenths of tenth parts.|
|The points of sinus versus.||Multiplication of sinus versus with the line to which.||The square root.||Decimal parts.||Decimals of de∣cimals.|
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 plun∣dered the people, and besieged the City with a Fleet. Marianus the Deputy op∣posed him; and there being a fight at sea, by an engine made by Proclus a most ex∣cellent 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 al∣so; 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 un∣worthy act to divulge it to the ignorant common people: yet let it go into the light, Page 376 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 Cylindri∣cal 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 de∣pends 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 mid∣dle, 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 no∣thing: 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 burn∣ing 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
To make a Burning-Glass of many Sphaerical Sections.
VItellio describes a certain composition of a Burning-glass, made of divers Sphaeral Sections: but what he writes he proves not, nor doth he understand what he says: whilst I was searching for that, I found this. Propound the distance of com∣bustion, let it be CB, let it be doubled, CA shall be the semidiamiter of the Sphaere, Page 377 whose Centre B must be extended to D, and the Diameter will be AD. Divide CA into four points, but the more the parts are, the more precise will be the de∣scription of the line, and set the numbers to the divisions: so setting the foot of the compass fast in I, and the moveable foot in B, make the semicircle EF, and mark it BI: and setting it in the 2. Centre at the same wideness, and the other movea∣ble foot in the line BD, describe another semicircle and mark it 3. and so to the fourth and mark it 4. Then setting the foot firm in B, at the distance of BC, or B4, make a circle, and the immoveable foot standing on the Centre B, upon the distance B3, describe another: so there is the third B, and the fourth BA, as BI. Then from the point, A, draw a line, and another from the point B; and let them meet in a point where the circled meets, with the semicircle 1. for let them be cut in G; then draw the second line from circle 2. and another from the same A the Centre, and let them meet, where the second circle cuts with the second semi∣circle in H; then from the third circle, and from B the Centre, and where they meet in, I, by the meeting of the semicircle: so from the fourth, where the fourth begins in K, and from KIHG draw a line, which shall be the Section to be described. The same may be done on the other part of the circle, the reason is this: The beam of the Sun LI falling upon the point I, of the Glass, is reflected to B, because B3. and BI are equal from the same circle: therefore the Angle B3I, is equal to BI3. But B3• is equal to 3IL, because it is subalternate, for the ray of the Sun LI is equidistant to the diameter of the circle, wherefore the Angles LI3 and 3IB, are equal, therefore it is reflected upon B. The same is to be said of the beam MH and NG, and this Glass is contrary to a Sphaeral Glass: From divers points of the circumference, the rays are reflected upon different parts of the diameter, and all the diameters are from the Centre: but in this the reflected beams unite, not in one point, and the diameter are various from the fourth of the diameter. But of this more largely in my Opticks. Lastly, I will not omit that the Cane doth kindle fire
Fire is kindled more forcible by refraction.
I Have spoken of Burning-glasses by reflection: Now I shall speak of those which burn by refraction; for these kindle fire more violently, I shall shew my reason in the Opticks. Wherefore
By a Cylindre of Crystal to kindle fire.
We may do it by setting it against the Sun, but very slowly and by leasure; for all the beams do not meet in one point, but in a line. The same way almost are we wont
To burn with a Pyramidal Crystal Glass.
But this burns about a line, yet both burn more strongly than a pillar Glass of a Py∣ramidal, in the place of this we may use a Vial full of water. But the most violent of them all, is with Page 378
A Crystal Sphaere, or portion of it.
And if a Sphaere be wanting, we may supply it with a Vial full of water, that is round and of Glass, set against the Sun: if you set behind it any combustible mat∣ter, that is friendly to the fire, so soon as the rays unite about the superficies, it forthwith kindleth fire, to the wonder of the Spectators: when they see fire rai∣sed from water, that is extreme cold, so will the portions of Sphaeres, as spectacles, lenticulars, and such like, which we speak of already.
A Crystal parabolick-Glass will kindle fire most vehemently of all,
we shall see it, because the beams all meeting, it kindles more than a Glass. We may also, as I said of a Glass
By refraction, kindle fire afar off,
And almost to infinite distance, as is demonstrated by Obtick reasons; and the more by how much as refractions work more forcibly than reflections: and I shall per∣form this many ways, as I said before, not onely by reason, but by experience. Almeon said, That he made the same way parallel lines cut a cross. I have said also, that if they be opposed in place, Crystal Sphaeres are so perfectly opposite by coition, as are Sphaeral and Cylindrical portions. Nor do they cast forth fire so far, that it is hard to believe it, and more than imagination can comprehend. Behold, I shall shew you a more forcible way to kindle fire. It sends forth also unequal, and com∣bust parallels. Let a uniform Section fall in, and it will carry forth oblique beams, you shall see the fire by a hidden and open beam, falling upon a right superficies, and it will come forcibly and uniformly into that place, where the beams unite most in a fit combustible matter: for if that combustible matter that is opposite, be not dry, it is in vain to set a Glass against it, either a Convex Cylindrical, or Concave Sphae∣rical; for the matter will be found almost pierced through with strong fire, and if it be not truly opposite it will burn, whether it be small or great. But it is considera∣ble, the portion of which it is. It will do also the same thing, if the thing be op∣posite, and be small or great, if need be.
In a hollowed Glass how the Image may hang without.
BEfore I depart from a plain Glass, it is performed by the later Artists industry, that in the same Glass many faces may be seen, or likenesses of the same Image, without any hindrance to the first: for behind it they make the Glass hollow, and make a little Concave, whence a foil being laid on, as I shall shew, and fitted well, it will hold another forth without. Hence comes it to pass by this excellent invention, that a man looking in a Glass, may see the upright Image of some other thing, and wonders at it, for catching at it, he can catch nothing but Air. I remember that I have often seen it, and the matter is thus. A Glass being made of Crystal, they make a hollow place on the backside like an Image, as curiously as they can; then they foil it over, and set it in its place, now as deep as the hollow is with in, so much will it shew it self without the superficies; and you cannot satisfie your self, unless you touch it with your hands, whether it truly stick without the Glass or not. So Letters are truly read, that they will seem to be made in Silver upon the Crystal; nor is the eye so quick, but it may be deceived when it looks on. Nor will I omit the Artifice,
To see in a plain Glass that which appears no where.
I have often much delighted my friends, and made them admire with this Glass. Provide thirty or forty little Tables ready, of a foot and half long, and two fingers broad, and a third part of a finger thick; so artificially hewed, that the thickness may be upon the one side, and the thinness on the other side, like the edge of a knife. Page 379 Place all these boards together, that the solid parts may stand altogether, as to make a perfect plain: Then paint your own Picture, or of some other thing upon it: yet by this artifice and great observation, that if the Image be neer the Glass, it must be drawn as it were afar off. If you would have it far distant, let the forehead be unmeasurably long, the nose somewhat longer, and the mouth, and the chin, like∣wise. The manner how to draw this Form exactly in Tables, I said in my Opticks. When the Image is now described, fasten the little boards upon a plain Table, that the head may be set downwards, and the chin upwards; and place the first Table after the second, and the second after the third, till they be all fastned. Hang the Table above a mans height, that no man may see into it, above the degrees of the Tables: and place a Glass over this, distant two foot from the Table, so long lift∣ing it up, and putting it down till you see the perfect Image. Now when any man comes neer the Glass to see his own Image, he shall see the Image of some other thing that appears no where. In the breadth of the Tables you may draw some Picture, lest they should give some occasion to suspect.
How Spectacles are made.
VVE see that Spectacles were very necessary for the operations already spoken of, or else lenticular Crystals, and without these no wonders can be done. It remains now to teach you how Spectacles and Looking-glasses are made, that every man may provide them for his use. In Germany there are made Glass-balls, whose diameter is a foot long, or there abouts. The Ball is marked with the Emril∣stone round, and is so cut into many small circles, and they are brought to Venice. Here with a handle of Wood are they glewed on, by Colophonia melted: And if you will make Convex Spectacles, you must have a hollow irondish, that is a porti∣on of a great Sphaere, as you will have your Spectacles more or less Convex; and the dish must be perfectly polished. But if we seek for Concave Spectacles; let there be an Iron-ball, like to those we shoot with Gun-powder from the great Brass Ca∣non: the superficies whereof is two, or three foot about: Upon the Dish, or Ball there is strewed white-sand, that comes from Vincentia, commonly called Saldame, and with water it is forcibly rubbed between our hands, and that so long until the superficies of that circle shall receive the Form of the Dish, namely, a Convex supre∣ficies, or else a Concave superficies upon the superficies of the Ball, that it may fit the superficies of it exactly. When that is done, heat the handle at a soft fire, and take off the Spectacle from it, and joyn the other side of it to the same handle with Colophonia, and work as you did before, that on both sides it may receive a Con∣cave or Convex superficies: then rubbing it over again with the powder of Tripolis, that it may be exactly polished; when it is perfectly polished, you shall make it perspicuous thus. They fasten a woollen-cloth upon wood; and upon this they sprinkle water of Depart, and powder of Tripolis; and by rubbing it diligently, you shall see it take a perfect Glass. Thus are your great Lenticulars, and Spectacles made at Venice.
How upon plain Concave and Convex Glasses, the foils are laid on and they are b•••ed.
NOw it remains that I speak of some few things, not to be overpassed of the band∣ing of Convex Glasses, and of foiling plain Glasses, and Convex Glasses, that so I may set down the perfect Science of Looking-glasses. First, for the terminating of Looking glasses, that are made of Crystal and Glass, then of other mixtures, and polishings, that a knowing Artificer may know, and know how to make them: For though amongst many things, that shew the Images of things, as water, some Jewels, and polished Metal do it; yet nothing doth so plainly represent Images, Page 380 as Lead foil'd upon Glass. Plain Looking-glasses are prepared of Crystal, and of Glass: those of Crystal are polished by wheels, and require another Artifice. But at Venice
How Glass Looking-glasses are made,
I have seen it. They take the melted Glass out with an Iron; with their blast they frame an empty Pillar; they open it on one side with their tongs, and whilst it is red hot they lay it upon a plain plate of Iron, that is equally made; and they put it into the furnace again, to make it softer; and that it may get the perfect plainness of the iron plate, they leave it over the furnace to cool by degrees: When it is cool, they do thus
Polish plain Glasses.
They fasten it upon a plain Table with Gyp; underneath lyeth a most polite plain plate of iron; they cast upon it the foresaid sand; they rub it with water by a stick, leaning thereon, until it be perfectly plain; they take it from the Table, and glew it on the other side, to polish them both: then they make them perspicuous, as I said they did. Now will I shew
To terminate plain Glass Looking-glasses.
Glass or Crystal Looking-glasses, when they are made plain and equal, the Artist makes a foil of the same bigness of Tin, that is level and thin, as perfectly as he can. For if Crystal or Glass had no foil of Lead behind it, by its strength and thickness it could never terminate our sight, nor stay the Image Printed upon it, but it would let it slip away; for Glass is pure and transparent, and so would not contain it, by reason of its brightness; and so the Image would vanish in it, as light in the Sun. Wherefore upon this foil you shall wipe over with Quick-silver, by the means of a Hares foot, that it may appear all as Silver: and when you see it fast on the superfi∣cies, you shall put it upon a fair white paper, and so upon the Glass; but first made clean with a linen clout, and polished: for if you handle it with your hands, the foil will not stick to it: with your left hand press down the Glass, and with the right take away the Paper, that the foil may cleave every where, and they bind fast toge∣ther; laying a weight upon it for some hours, and so let it stand and stir it not. Now I will shew
How a foil is put upon a Concave Glass.
But it is more laborious to lay a foil on a Concave-Glass: Prepare then a foil of the bigness of your Glass, that you shall lay upon the Convex superficies; and holding it fast with a finger of your left hand upon the Centre, with your right hand you shall fit the foil round about, and shall extend it on the said superficies, until it become of the same form with that convex superficies, and stick every where even unto it. Then of moist Gyp shall you prepare a form of the Glass, namely, by pouring Gyp upon the Convex superficies; and when the Gyp is dry, you have the form. Upon the form extend a foil of Tin, and let it agree perfectly with the form every where, because the form and the foil are made after the same superficies: strew quick-silver upon the foil, and as I said, make it stick by means of a Hares foot. The Artists call this Av•vare: put paper upon it, and pressing this upon the Glass, take away the paper; when you know it sticks fast, take away your hand, and lay on a weight, and after ••ke it away, but with a careful balancing of your hand, lest it take wind, and that the quick silver may all stick fast every where. Now remains how
To terminate Convex-Glasses.
Make Glass Balls, but of pure Glass, and without bladders as much as you can, as the receivers for distillations; and from the hollow iron that it is blown in by, let this liquid moisture be projected, namely, of Antimony and Lead; but the Antimony must be melted twice or thrice, and purged, and cast Colophonia in. So stir the mixture in the hollow vessel, and what remains cast forth: and so in Germany they make Convex-Glasses.
How Metal Looking-Glasses are made.
BUt Metal-Glasses are made another way. Wherefore if a Parabolical-Glass be to be made, draw a Parabolical line upon a brass or wooden Table; what is without it, must be filed away, that it may be equal, smooth, and polished: fasten it upon an Axis in the middle, and fit it with Instruments, that may be fitly turned about, let there be clay with straw under it, made up with dung, that the Table be∣ing turned about, it may receive a Concave form exactly; then let it dry, strew ashes upon it, and plaister clay above that, of a convenient thickness; let it dry by the fire, or if you will, by heat of the Sun, take it off, for it will easily part from the ashes: unite them together, that as much space may be between both forms, as you think fit, for the thickness of the Glass: when it is dry, cover it with this, leaving an open orifice on the top, and some breathing places, that the Air may breathe forth at it. Then make such a mixture; let them be put into a new pot that will en∣dure the fire, and lute it well within, that it may hold the faster; let it dry well, and do this twice or thrice over: set it to the fire, and melt in it two pounds of Tar∣tar, and as many of white Arsenick; when you see them fume, pour in fifty pounds of old brass, often used, and let it melt six or seven times, that it may be pure and cleansed; then adde twenty five pounds of English Pewter, and let them melt toge∣ther: draw forth some little of the mixture with some Iron, and try it, whether it be brittle or hard; if it be brittle▪ put in more Brass; if too hard, put in Pewter: or else let it boil, that some part of the Pewter may evaporate: when it is come to the tem∣per it should be, cast upon it two ounces of Borax, and let it alone till it dissolve into smoke; then cast it into your Mold, and let it cool: When it is cool, rub it with a Pumice-stone, then with powder of Emril. When you see that the superficies is perfectly polished and equal, rub it over with Tripolis. Lastly, make it bright and shining with burnt Tin; most adde a third part of Pewter to the Brass, that the mass may be the harder, and become more perspicuous.