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Thefe things being done, Itakcthc differences of cbe roots, of the great- eft to the fmalleft, for they are from 160.0.0. to 4 is. 6. 9. Make choice of themeafareof afoot, according to which diftances we would make our Glal's : let it be A B, which we divide into thirty parts ; and take twenty parts, namely, two thirds : I adde a line to it at right Angles, namely 8, and let it be BC, which I divide into fifty five parts. I divide one pirt into ten, and that one into ten parts more, and thofe arc tens of tens. Let A be nul , that is a cyfer , and there place fincy ; the fecond parr fixty one : the line joyned to right Angles, will be t wo ; the third pare fixty two; the line joyned to it will be five : fo the twentieth part will be eighty, and the line joyned to the Angle fifty fix : to the extremities of thefe lines I fatten a pin, and I put a brafs Cithern-wire upon them , and upon it I draw a line, and the Parabolical line is exactly defcribed by it ; for flhould we draw it without the help of this cord , it will be wavering, and not perfect. Then take a brafs Ta- ble of convenienc thicknefs, and draw the line now found upon it , filing away all that that fhall be above the line C A. Thefe things being done, take an iron rod of an cxait length, namely, twelve foot, as the line D C, and at the end fallen a plate, which Hull be for the circumvolution of the axis; at the other end faften a ipike, that it may be faftned fomcwhere , and be handfomely turned about. So being well fixed, we turn it about , by adding clay mingled with raw , that it may excellent
well make a hollow place , like to the ^.a c form of a Parabolical SeSion ; which be- rg^ r^-j M ing dried , we muft make another folid
JffT: one, that it may contlin the liquid Me- tal, as the maner is.
Chap. XVII.
A P 'ar Abohcul Sett ton that may burn to infinite dtfiance.
ZOmmtm the Greek, writes in the third Tome of his Hiftories , That Anaftafiut moved fedition againft VitaliAnm a Thracian , and he got thofe of Myfia , and the bcythians to If and with him ; and in the Country by Conftantinople , he plun- dered the people , and beficged the City with a Fleet. pofed him ; and there being a fighr at fea , by an engine made by Vrodtu a moft ex- cellent man, for he then was famous for Philofophy and Mathematicks ; for he not onely knew all the fecrets of the moft eminent Artificer, jirchmedes , but he found out fomenew inventions himfclf ; the enemies Navy was vanquifhed. For *Procl$u is reported to have made Burning-Glafles of brafs, and to have hanged them en the wall againft the enemies Ships ; and when the Sun beams fell upon them, that fire brake forth of them like to lightning, and fo burnt their Ships and men at fea, as Dion reports that Archimedes did formerly to the Roman s befieging Syracufe. But I will fhew you a far more excellent way than the reft , and that no man as ever I knew writ of , and it exceeds the invention of all the Antients, and of our Age al- fo;and I think the wit of man cannot go beyond it.This Glafs doth not burn for ten, twenty, a hundred, or a thoufand paces, or to a let diftance, but at infinite diftance : nor doth it kindle in the Cane where the rays meet , but the burning line proceeds rom the Centre of the Glafs of any Longitude, and it burns all it meets with in the vay. Moreover, it burns behind, before, and of all fides. Yet I think it an un- vortby a& to divulge it to the ignorant common people : yet let it go into the light,
that
Natural Maqick. jBgo^ 17.
that the immenfe goodnefs ©f our great God may be praifed , and adored. Becaufe a proportional Radius doth proceed frcm the greater Section, from the lefs is made the greater: to avoid this, make it of a Cylindrical Se&ion, for it is the mean, and let it be fet for the axis of the fmall andcf the greater deflection , which may pafs through the middle parallels : this held againfr the Sun, doth make refraction of the beams fern into it, very far, and perpendicularly from the Centre of a Cylindri- cal Section; and in this Art thcrcafon cannot be found , that the beams uniting (houldpart again : Wherefore it receives them direftly , which it fends back again obliquely into beams far frcm the fuperficies of it. For the beams pafling 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 feems cleared , which will be neer the Centre , nor is it far diftant from the point where the rays meet; but neer the ray coming forth from that point , from the fuperficies of the Glafs, called Parabolicall , which muft remain firm in that place which I faid before. Let experiment be made of its venue , by threds pafling frcm its Centre, or iron wire, or hair j and it is no matter whether it be Parabolical or Spharrica] , or any Section of the fame order : then let it be excellent well fitted upon the Cemfe of the laid Section: If the rays go forth above, or a little beneath, it is no matter, if not much money, or much money be laid ouc to make it. The making of it de- pends meerly on the Artificers hand ; the quantity is nothing, be- it fmall or great. The Latitude of the hollow is not neceffary, onely let it be lent forth frem the mid- dle, that the rays may meet excellent well in the Centre. Let the window be made open afliunr ,. that it rmy receive a Parabolical Glafs; and thus fhall you have a Glafs, if that be Well done I fpake of. He that bath ears to bear, let him hear • I have not fpoken barbaroufly , nor could I fpeakmore briefly, or more plainly But if a fmall one do not anlwer a great one in proportion, know that you will operate no- thing: let it be large about the bafis, fmall at the top, equidillantto the Frft. Let it not be a fteel Glafs, becaufe it cannot fuftain the heat of the burning , and by burn- ing it lofeth its brightnefs. Let itbe therefore of Glafs a finger thick: Let the Tin foil be of purged Antimony, and Lead, fuch as they make in Germany : let the form be of clay : put the Glafs upon it , and melt it in a Glafs furnace, that it may
take its form. This is a wonder, that that ' which caufeth fo much burning in the work, is cold, or at mcftbut luke-warm. If yon would have it burn before, of the Section which is about the bafis, make a circle, in the middle point whereof fit the Artifice, that the ray returning, may come forth* to' the fore parr. This I have faid ; and I have obferved, that we may ufe this Artifice in great and wonderful things , and chiefly by inferibing letters in a full Moor. For what- foever we have written by this Glafs , as I faid of a plain Glafs , we may fend letters of it to a very great diftance : and becaufe I faid it fends forth to infinite diftance, it is fent as far as the Moon , efpecially being helped by its light.
lidj y*W JH?Us2x-jt i' .fit 1*1 * UOV v* ?rDifi'/. I
Chap. XVIII.
To maj>e a Bftrning-Glafs of many SyhtTicxl SeRions.
"\Tltellio defcribes a certain compofition of a Burning-glafs, made of divers Sphaeral Sections : but what he writes he proves not, nor doth he underfiand what he fays: whilft I was fearching for that, I found this. Propound the diftance of com- bufiion, let it be C B, let it be doubled, C A (hill be the femidit miter of the Sphere,
whofe
Of flrange (flajfes.
whole Centre B muft be extended to D, and the Diameter will be A D. Divide C A into four points, but the more the parts are , the more prccife will be the de- fcriptioncf the line, and fet the numbers to the divifions: fofettingthe foot of the compafsfaft in I, and the moveable foot in B, make the femicirdc EF, and mark it B I : and fcttingit in the ^. Centre at the fame widenefs , and the other movea- ble foot in the line BD, defcribc another femicirclc and mark it 3. and fo to the fourth and mark it 4. Then fctting the foot firm in B , at the diitance of B C, or B 4, make a circle , and the immoveable foot (landing on the Centre B , upon the diitance B 3, defcribc another: fo there is the third B, and the fonrth B A, as B I. Then from the point, A, draw a line, and another from the point B ; and let them meet in a point where the circle I meets , with the femicirele 1. for let them be cut in G ; then draw the fecond line from circle 2. and another from the fame A the Centre, and let them meet, where the fecond circle cuts with the fecond femi- circlc in H • then from the third circle, and from B the Centre, and where they meet in, I, by the meeting of the femicirele : fo from the fourth, where the fourth begins in K, and from K I H G draw a line , which fhall be the Section to be defcribed. The fame maybe done on the other pan of the circle, thereafonisthis: The beam of the Sun L I falling upon the point I, of the Glafs, is reflected to B, becaufe B3. andBl are equal from the fame circle: therefore the Angle B 3 I, is equal to B I 3, But B 3 I is equal to 3 I L , becaufe it is fubalternate , for the ray of the Sun L I is equidiflant to the diameter of the circle, wherefore the Angles L I 3 and 3 I B, are equal , therefore it is reflected upon B. The fame is to be faid of the beam M H and N G, and this Glafs is contrary to a Sphaeral Glafs : 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 refie&ed beams unite, not in one point, and the diameter are various from the fourth of the diameter. But of this more largely in my O pucks. Laftly, I will not omit that the Cane doth kindle fire
circularly , when that as far as this circle it kindles in a point. Divide the Parabo- lical line by finm verfiu, and let them meet upon contrary parts. For example, lec the Parabolical Section be C E F,they?«M verfm D E : cut this circumference in E, and let C F meet together in the manner they flood before, that it may be E G F E, and about the axis G H turn it round , there will be made a round Cane, make it of Steel , or other Metal ; and polifh it, and it will kindle fire round about.
Chap. XIX. Fire it kindled more forcible by refrattion.
I Have fpokenof Burning-glafTes by reflection : Now I fhall fpeak of thofe which burn by refraction; for thefc kindle fire more violently , I fhall fhew my reafon in the Optick?. Wherefore
By 4 Cylindre of Cryfttl to kindle fire. We may do it by fettingit againft the Sun, but very (lowly and by leafure • for all the beams do net meet in one point, but in a line. The fame way almoft are we wont
Tobttrnmtha Pyramidal CryfiaKjUfs. But this burns about a line , yet both burn more ftrongly than a pillar Glafs of a Py- ramidal , in the place of this we may ife a Vial full of water. But the tnoft violent of them all, is with
E e e i/1
278 Natural Magick. BooJ^ 17.
{ryftalSphare, or portion of it.
And if a Sphere be wanting, wc may {"apply it with a Vitlfullof water, that is round and of Glafs , fet againft the Snn : if you fet behind it any combuftible mat- ter, that is friendly to the fire, fofcon as the rays unite about the fuperficies, it forthwith kindleth fire , to the wonder of the Spectators : when they fee fire rai- fed from water ,that is extreme cold, fowill the portions of Sphxres, as fpedtades, lenticulars, and fuch like, which we fpeak of already.
A Cryflal parabolick^Glaft wtU kindle fire moft vehemently of all, we (hall fee ir,becanfe the beams all meeting, it kindles more than a Glaf?. Wc may aifo, as I faid of a Glafs
By refraction, kindle fire afar ojf9
And almoft to infinite diftance, as is demonftrated by Obtick reafons ; and the more by how much as refractions work more forcibly than reflections : and I ftiall per- form this many ways , as I faid before , not onely by reafon, but by experience. j4/meon(*\d, That he made the fame way parallel lines cut a croff. I have faid alfo, that if they be oppofed in place, CryftalSph acres are fo perfectly oppofite by coition, as arc Sphaeral and Cylindrical portions. Nor do they caft forth fire lb far , that it is hard to believe it, and more than imagination can comprehend. Behold, I (hall (hew you a more forcible way to kindle fire. It fends forth alfo unequal, andcom- buft parallels. Let a uniform Section fall in , and ir will carry forth oblique beams, ycu fhall fee the fire by a hidden and open beam, falling upon a right fuperficies, and it will come forcibly and uniformly into that place , where she beams unite moft in a fit combuftible matter : for if that combuftible matter that is oppofite , be not dry, it is in vain to fet a Glafs againft ir, either a Convex Cylindrical , or Concave Sphe- rical j for the matter will be found almoft pierced through with ftrong fire , and if ic be not truly oppofite it will burn, wh^rher it be fmall or great. But it is considera- ble, the portion of which it is. It will do alfo the fame thing, if the thing be op- pofite, and be fmall or great, if need be.
Chap. XX.
In a hollowed Glafs how the Image may hung without.
BEfore I depart from a plain Glafs , it is performed by the later Artifts induftx^, that in the fame Glafs many faces may be feen, or likenefles of the fame Image, without any hindrance to the firft:for behind it they make the Glafs hollow, and make a little Concave, whence a foil being laid on, as I fiiall Anew, and fitted well, it will hold another forth without. Hence ccmes it to pafs by this excellent invention, that a man looking in a Glafs , may fee the upright Im:ge of feme other thing v and wonders at it , for catching at it , he can catch nothing but Air. I remember that I have often feen it , and the matter is thus. A Glafs being made of Cryflal , they make a hollow place on the backfide like an Image, as curioufly as (hey can ; thej» they foil it over, and fet it in its place, now as deep as the hollow is with in, fomucti will -it fhewitfeff without the fuperficies j and you cannot fatisfieyour felf , unlefs you touch it with ycur hands, whether it truly flick without the Glafs or nor. So Letters are truly read, that they will feem to be made in Silver upon the Cry ftal ; nor is the eye fo quick, but it may be deceived when it looks on. Nor will I omit the Artifice, : *rn;: ■' ;>