The next burning mirror that seems to have been con structed after that of Archimedes, was contrived by An themius of Tralles, who flourished towards the end of the fifth century. This learned architect was a favourite of Justinian, who employed him in the construction of various edifices, but particularly in the church of St So phia at Constantinople, which he designed and executed. lie was also the disciple of Proclus, from whom he pro bably received some information respecting the construc tion of burning mirrors, of which he has given a full and distinct account in a fragment, entitled riqr 7i-xlc`o:Iedy F.zza/.0..w.credv. " Of Wonderful Machines," which has been translated and illustrated by M. Dupuys, in the Memoires de l'4cadenzie des Inscriptions, 1777, tom. xlii. p. 392-451. The following quotation from this frag ment, will give the reader a complete view of the inven tion of Anthemius, who appears to have been completely master of the subject upon which he wrote. After ac knowledging, that it was universally admitted in his time, that Archimedes had destroyed the Roman fleet by means of burning mirrors, Anthemius observes, " Let us, there fore, bring and collect at one point other different rays, by means of plain and similar mirrors, in such a manner that all these rays, united after reflection, may produce inflammation : This may be effected by means of several persons holding mirrors, which, according to the posi tions indicated, send the rays to one point.
" But, in order to avoid the embarrassment resulting from entrusting this operation to several persons, (for we shall find, that the matter intended to be burnt does not require less than twenty-four reflections,) the following construction must be followed : Let there be a hexago nal plain mirror, and other adjoining similar mirrors at tached to the sides of the hexagonal mirror by the small est diameter, so that they may be moved on these lines by means of plates or bands applied, which unite them to each other, or by means of what are called hinges. lf, therefore, we bring the surrounding mirrors into the same plane with the mirror in the centre, it is clear, that all the rays will undergo a reflection similar, and confor mable to the common position of all the parts of the in strument. But if, the centre mirror remaining as it were immoveable, we dexterously incline upon it all the other mirrors which surround it, it is evident that the rays reflected by them will tend towards the middle of the place where the first mirror is directed. Re peat the same operation, and around the mirrors already described placing other similar mirrors, all of which may be inclined towards the central mirror, collect towards the same point the rays which they send, so that all these united rays may excite inflammation in the given spot.
" But this inflammation will take place better, if von can employ for this purpose four or five of these burn ing mirrors, and even seven, and if they are all at the same distance from the substance to be burnt, so as that the rays which issue from them, mutually intersecting, may render the inflammation more considerable : For, if the mirrors are all in one place, the rays reflected will intersect at very acute angles; so that all the place around the axis being heated, the inflammation will not take place at the single point given.
" It is therefore possible, by means of the burning mirrors just mentioned, to carry inflammation to a given distance. Those who have made mention of the mir rors constructed by the divine Archimedes, have not said that he made use of a single burning mirror, but of several ; and I am of opinion, that there is no other way of carrying inflammation to any distance." From the demonstration which Anthemius proceeds to give, but which we have not room for inserting, it ap pears that his mirror was constructed on exact geome trical principles, and was truly parabolic.
About the end of the sixteenth century, when an ar dour for science began to prevail, we find the subject of burning mirrors again brought into notice. Our coun tryman, Leonhard Diggcs, in a work entitled Pantome tria, published in London in 1571, and republished by his son Thomas Digges in 1591, mentions a burning mir ror, which appears to have consisted of a combination of plain mirrors. In the Preface to the second edition, Mr Thomas Digges observes, " Archimedes also (as some suppose,) with a glasse framed by reuolution of a section parabolical', fired the Roman name in the sea, comming to the siege of Syracusa. But to leave these celestial causes, and things donne of antiquitie, long agoe, my father, path at sundrie times, by the sunne beanies, fired powder and dischargde ordinance half a mile and more distante ; which things I am the boulder to report, for that there are yet lilting diverse of these his doings (oculati testes, eye witnesses,) and many other matters farre more strange and rare, which I omit as impertinent to this place." In the 21st chapter of the first book, the subject of burning glasses is resumed. " Some have fondly sur
mised, that Archimedes burned the Roman nauie with a portion of a section parabolical artificiallye made to re flect and unite the sunne beanies a great distance off, and for the construction of this glass toke great peines, with high curiositie, to write large and many intricate demonstrations, but it is a mere fantasie and utterly im possible, with any one glass whatsoeuer it be, to fire any thing only one thousand pace off, no though it were an 100 foote over, marry true it is the parabola for his small distance, most perfectly cloth unite beanies, and most vehemently burneth of all other reflecting glasses. But how by application of mo glasses to extend this unitie or concourse of beames in his full force, yea to augment and multiply the same, that the farder it is carried the more violently it shall pearse and borne. Hoc opus, hic labor est, wherein God sparing life and the time which opportunitie seruing, and minde to impart to my coun trymen some such secrets, as bath I suppose in this our age been revealed to very few, no lesse seruing for the securitie and defence of our natural' countrey, than surely to be maruailed at of stram2;ers." A few years after the publication of the Pantometria of Leonhard Digges, our illustrious countryman Baron Napier of Merchiston, drew up a list of " secret inven tions, profitable and necessary in these days for the defence of this island, and withstanding of strangers, enemies of God's truth and religion." The first and second of these inventions are burning mirrors, which Lord Napier has very briefly described in the following words : First, "The invention, proof, and perfect demonstra tion, geometrical and algebraical, of a burning mirror, which receiving of dispersed beams of the sun, cloth re flect the same beams altogether united, and concurring precisely in one mathematical point, in the which point most necessarily it engendereth fire ; what an evident demonstration of' their error who affirm this to be made a parabolic section. The use of this invention serveth for the burning- of the enemy's ships at whatsoever ap pointed distance." Secondly, "The invention and sure demonstration of another mirror, which receiving the dispersed beams of any material fire, ur flame, yieldeth also the former ef fect, and serveth for the like use." It does not appear that Napier ever condescended to give any farther account of these burning mirrors ; for when he was solicited, a short time before his death, by one of his most particular friends, " not to bury such ex cellent inventions in the grave with him," he replied, " that for the ruin and overthrow of man there were too many devices already framed, which, if he could make to be fewer, he would with all his might endeavour to do; and that therefore seeing the malice and rancour rooted in the heart of mankind, will not suffer theni to diminish the number of them, by any new conceit of his, they should never be increased." The next burning mirror of which we have any ac count, was invented by the learned Athanasitts Kircher. This indefatigable philosopher made a great variety of experiments, for the purpose of establishing the authen ticity of Archimedes's burning mirrors. Ile began with combining a number of parabolic specula; but this me thod was quickly abandoned, and he resorted to the use of plain mirrors. I laving procured a number of plain and circular glasses, he placed them upon a wall, at such degrees of iodination that they all reflected the light ul tile sun to one puha, and produced a consider able heat. His principal experiments, however, were made with live plane spi.cula fixed in a frame, so that they collected the solar rays at the distance of more than one hundred feet. At this distance he produced a degree of heat which sufficiently convinced him, that by increas ing tire number of his mirrors, lie could have consumed inflammable substances at a much greater distance. lic informs us in his Magica Catolarica, that the heat of the first reflection was different from that of direct light ; that the light when doubled gave a very perceptible in crease of heat ; that it had the heat of a fire when tri pled; that when quadrupled, the heat could still be en dured; but that a fivefold reflection made the heat ahnost intolerable. From these results he concludes, that a combination of plain mirrors was capable of producing more powerful effects, than mirrors of a parabolic, hy perbolic, or elliptic form ; and he entreats future ma thematicians to prosecute the subject with a more nu merous combination of plane specula. Not satisfied with these trials, Kircher, accompaned by Iris pupil Schottus, made a voyage to Syracuse in order to exa mine the position of the hostile fleet, and they were both completely convinced, that the ships of Alarcellus could not have been more than thirty paces distant from Ar chimedes.