Section 84

CHAP
Natural Magic k. 2>00^ 17.
Chap. XII. How we may jce in a Chamber things that are net.
I Thought this in Artifice cot to be dtfpifed: for we nay in my Chamber , if a man look in , fee thofe things which were never there ; and there is no man fo witty that will think he is mittaken : Wherefore to defcribe the matter, Let there be a Chamber wherein to no other light comes , unlcfs by the door or window where the fpc&ater looks in : let the whole window or part of it be of Glafs, as we ufe to do to keep out the cold ; but let one part be poliftied, that there may be a£ooking- glafs on both fides, whence the fpe&ator muft look in ; for the reft do nothing. Let Pi&urcs be fct over againft this window , Marble ftatues , and fuch-iike ; for what is without will feem to be within , and what is behind the fpe&ators back , he will think to be in the middle of the Honfe , aa far from the Glafs inward , as they ft and from it outwardly , and fo clearly and certainly, that he will think he fees nothing but truth. But left the skill ftiould be known , let the part be made fo where the Ornament is, that the fpe&ator may not fee it , as above his head , that a pavement may come between above bis head : and if an ingenious man do this , it is impotTible that he fhould rappofc that he is deceived.
Chap. XIII. Of the eperations of a Cryftal Pillar.
NOr fhallthe operations of a Cryftal Pillar go unfpoken of , for in it there arc fome fpeculations not to be defpifed. Firft,
7# kindle fire with a Crjfial TiUar,
by oppofingit to the Sun, it will kindle fire behind ic about the circumference: off- tiroes lefc above the Chamber , when the Sun fhined, it burnt the Blankets. They that will at fct hours and places burn the enemies camps , if it be laid upon fuel for fire, it will certainty kindle ir. We may alfo
With a Cryfial Pillar, make an Image hang in the Aire. It will fcew the Image hanging in the Air, both before and behind. Let the Obje& 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 wr-cre from the Pillar, clearly and perfpicuoufly j and if thevifible Obje& be between the eye and the Pillar, the Image will appear behind the Pillar, as I faid. If it be a very vifible Qbje&, as fire or a candle, the matter is feen more clearly without any difficulty : I gave the reafons in my Opticks. We may alfo
In a Cryft*l Pillar fee many %ain-bows. Make a folid Pillar in a Glafs furnace, fo great as a Walnut , and let it be made round onely by the fire, as the manner is, as Glafs-makers ufe to do , that without any help of the wheel, the outward fuperficies may be moft polite : where the Iron touched it, there leave a Pedeftall. It is no matter for pure Glafs, for impure is beft « place this upon your eye, and a burning candle over againft it ; the light refra&cd by bladders will fhr w infinite Rain-bows, and all the light will feem Golden-colour'd, that no- thing can be more pleafant to behold.
CHAP*
Of Jtrdnge (flajfes
?7
Chap. XIV. Of Bnrmng-Glafcs,
] Proceed to Burning- Glaffes , which being oppofed againft the Sun beams, will kindle fire upon matter laid under them ; Intbefealfo are the greateft fecrets of Nature known. I fhalldefcribe what is found out by Ettc Ude, 'Ptolemy , and Ar- chimedes • and I (hall add our own inventions , that the Readers may judge how far new inventions exceed the old. Fire is kindled by reflexion, retraction, and by a fimple and a compound Glats. I fhall begin from a fimple rcfle&ion, and from
A Comave-Glafs that fhall kindle fire behind it :
which few haveobferved. Know, that a Concave-glafs will burn from its middle poinr,m«o the hexagonal-fide above the Glafs, as far as a fourth part of its diame- ter; from the hexagonal-fide, as far as the te- tragonal without the Glafs, on the lower part of it : Wherefore cut cff that part of the fcmicircle, which is fituate from a pentagon as fat as a tetragon, as it were the band of the circle ; and this being polifhed , and oppofed againft the Sun , will caft fire far from it , be- ; hinde it. 1 will fay no morc,becaufc I laid more at large in my O pricks concerning this. So al* fo we may
With a Concave Pillar or Pyramidal, kindle fire: but very flowly, with delay onely, and in the Summer-Sun % it kindles in the whol* line, and not in a point, but being extended by the point of accenfion of its circle*. The fame will fall out by a Pyramidal Concave.
Chap. XV. ^ (
Of a Parabolical Sett ion, that u of altGlaJfes the ntotf burning.
THat is called a Parabolical Se&ion, that more forcibly farther off, and in fliort- enime, will fet matter on fire , that is oppofite to it: it will melt Lead and Tin : My friends related to me, that Gold and Silver alfo ; but 1 have made them red hot. By which invention of &4rchtmedcst as appears by the teflimony of Galen, and many more, We read that he fet the Roman Navy on fire, when Marcetm befieged Sjracnfe, his Country. Plutarch in the life of Pompliui faith, The fire that burnt in Diana's Temple, was lighted by this Glafs, that is, by inftrurrents that arc made of the fide of right triangle, whofe feetarcequal : Thefe made hollow, dofrom the cir- cumference refpefl one Centre. When therefore they are held againft the Sun, fo that the beams kindled may be gathered from all paits> andbe united in the Centre, and that they do fever ihe Air ra rifled, itfoon fets on fire all fuel that is combu- flibie oppeled againft it , by kindling firftthe li^hteft and drieft parts ; the beams being as fo many fiery dans fallingupon the Object. In a Concave fpherical Glafs the beams meeting together, kindle fire in * fourth part of the diameter under the Centre, which are directed within the fide of a Hexagon from the fuperficies of the circle. But a Parabolical Section, is, wherein all the beams meet in one point from all the parts of its fuperficies. Cardarut teachcth how fuch a Glafs thoold be made* If we would kindle fire at a mile diftance , we muft defcribc a circle, whofe diame- ter muft be two miles longhand of this we muft take fuch a parr, that the roundnefs of it may not lye hid5camely, a fixtieth parr,to which we muft add a dimetient,acccrding to the altitude in one point , and upon the fixt diameter muft we bring about part of the circle , which fhall delcribe the portion of a Sphere ; which when we have po-
Ddd* iTfhed,
Natural Magick. ©00^17.
lifhcd, if wc hold it againft the Sun , it will kindle a moft violent fire a mile off. *Tis Grange bow many follies he betrays himfelf guilty of, in thefe words. Firft, he pro- mifeth a Glafs (hould burn a mile off ; which I think is impolfible to burn thirty foot off, fork would be of a wonderful vafinefs; for the fupcrficies of the Cane is fo plain,& to receive any crookednefs, it can hardly be made fo great. Moreover, to de- scribe a cirde,wliole diameter fhould be two miles long,whac compares muft we ufe, and what plate ihall wc make it on,or whofhtll draw it about ?And if it be truc,thac Jrchimcdet by a Parabolical Glafs did burn (hips from the wall,the diftance could not be above ten paces,as appears by the words of theAuthors themfelves;for in the fame plate he railed (hips , and threw them againft the Rocks : and his engines were Iron bars, the greater} part whereof lay backward • and by reafon of thofe iron crews, it is manifeftit could be done no other ways. There arc other fooleries,but I pafs them for brevity lake, that I might not ieem tedious: the caufeof his error was, that he never had made any fuch Glafles ; for hid he tried it, he would have fpokc other- wife. But I will now (hew how
To make a Glafs out of a ^Parabolical Sell ion. V -J . . .
1 he way to defcribe it is this : Let the diftance be known how far we would have the Glafs to born, namely, A B ten fooc ; for were it more, it could hardly be done : double the line A B. and make A E C, the whole line will be A C : from the point A , draw a right line D A, and let D A and A E be equal one te the other, and .ajt at ri^ht Angles by AC, but both of them muft be joined to the quantity AC, as D C E, which in C make a right Angle, D C E. Therefore the Triangle D C E is a right angled Triangle , and equal fides: and were this turned about the Axis C Dentil it come to its own place whence it parted,therc would be made a right an- gled Cane , EDNC, whofe Parabolical Se&ion will be A B C : the right line D C will be the Axis of the Cane , and CE (hallbethefemidiamcter of thebafisofthe Cane: Through the point C you muft draw a line parallel to D E , and that is HI of the length ofC EandC D ; and by the point B draw another parallel to thefaid line E D, which is F B G;and let B G and B F be bothof them equal to A C : fo F G (hall be the upright fide , and H I the bafis of the Parabolical Se&ion : If therefore a line be drawn through the points HE AG I, that (hall be a Parabolical Section,
the Diagram whereof is this that follows.
But if you will burn any thing, you muft rot make your Parabolical Glafs to the bignefs of the whole line H FA G I, but onely take a part thereof, as if we would take the top part of it LAM, that the line L M may cut A C in K, or greater or leffer : if you will make ore greater, cut off A K beneath itjfor the bigger it i?,the more quickly and vehemently wil it burn; if you will have it lei>>rake it above A K.
But thus ycu muft do, that the crooked line L A M may be more exadtly defcribed , that you may not commit the leaft error. Wherefore on a plain Table I protraft the line ABC, and let A B be double\he diftance, that we intend to burn any thing, that is, the length of the line ABC: trcm the point B, I raifea perpendicular line BD,thc altitude whereof muft be of the lame femidiameter of the Se&ion to be made,that is the line L M, the half whereof is LK ; from thence defer i be a lemicirele, whofe beginning A muft pafs through the poiat D.But you (hall find the Centre thus : Let the points A D be joyned by a line, and let the Angle B A D be made cqnal to A D E, and the line D E drawn forth, (hall ckAC in F,that(hall be the Centre : fo draw the femicircle ADC. If there- fore weT(hall cut the line B C into fmaller parts , fo much the leffer Parabolical line muft be defcribed. Divide it into four parts , and let the points of the divifions be H G F : then defcribe three circles , that (hall be termined.by A from the three points HGF : the firft is A F, the fecond A G, the third AH: and they fhill cut
Of ftrange (jlajfes.
Pi
2FC H
line B D ; the firft in F, the fccond inG, the thir' in H • thence I take my Seaion to be perfc&ed LKM, and I cut the line K A into (our parts, and thorow thofc points I draw parallel lines to LM.Lec BH be the neereft to the top of the Parabolical Sea ion, the fccond BG that lollows next, and thethird BF next to that, and afrer fhall be L M. Thence by the lines LFG HA, draw a crocked line, and do the fame on the other part fo far as M, and that fhall be the line fought for, to make the Pa- rabolical Seaion , and from that muft be made the Glafs, as I fhall fhew.
Chap. XVI.
Hot* a FarabolicalSettion may be dejeribed, that may burn obliquely , And at a very
great diftance.
f
IHa ve defcribed a Parabolical Seaion , which might be made by rule and compafs, becaufe we may ufe it at a fhort diftance ; but in greater diftance we muff proceed by numbers : as for forty or for fixty foot , and not much more, left the GUfs fhould be made of an unufual magnitude. The forefaid Glafs burns between it and the Sun j and if the Sun be not as you defirek, the operation is loft : fo alfo by an oblique Glafs, that is between the Sun and the combuftible matter,or over againft it.Whence according to the fituation you may ufe them all , namely, wherein they anfwer your expeaation } and efpecially when the Sun is in the Meridian , they burn with more vehemency. This I muft tell you,that you may not be deceived jfor when you erre, you commonly draw others into error with you. A Parabolical Glafs made from the top, if the Seaion fhall be from the top, if we would burn far, the Glafs will be plain ; and that it may have fome crookednefs , it will be wonderful great. And if the Seaion be about the bafis, that will be worft of all ; for from the leaft diftance, it will be aimcft flat : wherefore that we may have it with fome crookednefs , we muft take a line about the neck of the Seaion, not the head, nor the feet. Where- fore being to make a Glafs of a Parabolical Seaion , about the neck of the Seaion, where thegreateft crookednefs of the Parabolical Seaion is made, and that may burn far from its fuperficies, to twenty foot diftance ; Let the line A B be the firms verfru eighteen foot long : from the point A, I raife a line to right Angles with A B, which fhall be the line by which,the fourth part whereof is A B : cut A B in C,and let it be two foor,and C B fixteen footrl multiply twice feventy two,and that makes one hundred forty and four : the fquare root of this is twelve ; wherefore the line ere- fted perpendicularly from the point C, unto the circumference of the Parabolical Seaion , will be D I of twelve foot, wherefore C I will be the line appointed: joyn
I B, and the Radius that muft burn, will be in the point B that was fought for: ■£j Wherefore the ray of the Sun , that is e - quidiftant to the firm verfm H I, is rcfle - fled by IfB inB; the Latitude whereof will be about twenty foot : for the line I C of twelve foot, multiplied into it felf, will make one hundred forty and four j and C B is fixteen foot, which multiplied into it felf , makes two hundred fifty and fix; addethefe together, andtheymake four hundred : the fquare root of it is twenty foot, thus. Wherefore I am rcfolved to takethe part of the Glafs , intercepted between the points I and F, and I feek two thirds of orefoor, from C toward B, and I divide one foot into thirty parts, that the crookednefs may be taken more precifely • and let C ® be twenty parts of
afoot,
574 Natural MagicK.
a foot, fr^m A to C fixty p*Ks, became they arc twofoo^ : wherefore from A to G, where we ttnil make our G afs, will be eighty parts. Wherefore let us begin from A G fixty parts, to which I always add four cyfers oooo. for this purpofe, that When numbers come tortb,wt!ofe roots cannot be extra&e'd , thofe that arc taken may be to the leaft lots : wherefore we (hall make the Table under written. In thefirft line are the points of the [ir,m verfw : in the fecond, the fqares, the lines to which ; from tb vvefl^l! reduce ihefe to pans, by multiplying by thirty , there comes forth 2160: mu.aply bv the parts of the finm verfm A C, there will arife 1 29600 : in the third line are too?' of the forefaid number, namely, the lines appointed: adding there* fore to 1 20600, four cyfers, they make 1196000000: the fquare root of this is 3 6 000, of which laft cyfers, one fignifies the tenth part of afoot, another the tenth ot a tenth part : thus, 3 6 0.0.0.0. lb will be the forefaid Table made.