126 MR JOHN SCOTT ON THE BURNING MIRRORS OF ARCHIMEDES. 



tion to these defects, and to remedy them proposes that a telescope and some- 

 what complex apparatus be attached to each reflector, that with fewer hands the 

 adjustment might be rendered more accurate and speedy. 



It is obvious that the improvement suggested by Peyrard is only partial and 

 its success doubtful. I conceive the Archimedean mirror to have been a compound 

 reflecting apparatus, free from these defects, capable of being directed by one eye 

 and guided by a single hand. From Tzetzes we learn that the mirror was hexa- 

 gonal, that like Buffon's it consisted of a combination of reflectors, and that at 

 proper distances from the outer mirror were placed other smaller ones of the 

 same kind. This last peculiarity of the Archimedean mirror has no parallel in 

 that of Buffon ; and yet the arrangement of the smaller mirrors, at proper dis- 

 tances from the larger, indicates that the relation of the two kinds to each other 

 formed an essential feature of the combination. Although the above passage 

 conveys no information respecting the nature of the specula, there is such a de- 

 scription of the connection of the parts as an intelligent observer might carry 

 away, and yet be unacquainted with the scientific principles involved in the 

 construction. 



In the sequel (Arts 13 and 14) we show how larger and smaller specula, all 

 of the same kind, can be so connected as to form a single compound reflector 

 capable of concentrating on a single spot the reflected rays, and of darting them 

 instantaneously in any direction, when they will produce the effects ascribed to 

 the mirror of Archimedes. The results thus being the same, and the construction 

 of the combination coinciding with the description given by Tzetzes, we 

 therefore infer that the real principle of the Archimedean mirror has been 

 attained, and that the accounts which have come down to us respecting it are in 

 the main authentic. This will be brought out more fully after the following 

 general propositions have been considered. 



For the historical facts contained in the preceding, I am chiefly indebted to 

 Peyrard's edition of the " Works of Archimedes," and to the article " Burning 

 Glasses," in the Encyclopaedia Britannica. 



Akticle I. — Prop. When the Light emanating from a Luminous Sphere of small angular 

 diameter falls on a very small Plane Mirror ; to find the Intensity of the reflected Light 

 at any distance from the Mirror. 



Let GH (fig. 1, Plate III.) be the mirror, B the point of reflection, AC the small 

 luminous sphere, and DE the plane on which the reflected light falls. It follows, 

 as a consequence of the equality of the angles of incidence and reflection, that the 

 angle which DE subtends at B is equal to that which AC subtends, DE being 

 supposed perpendicular to the cone of rays reflected from B. 



