144 MR JOHN SCOTT ON THE BURNING MIRRORS OF ARCHIMEDES. 



Article 13. — Prop. The Rays which converge to the focus of the exterior Parabolic Mirror 

 may be thrown by a second reflection on a given circular space, by constructing the interior 

 reflector in the following manner : — 



Let DH and H'D (fig. 17) be parts of parabolas, whose common focus is/, their 

 axes being respectively /C parallel to RG, and/C to QG. 



By causing these to revolve about the line /A, a surface will be described, such 

 that the rays converging to/ and falling on DH, will be reflected parallel to /C, 

 and fall on the plane FF'. 



In like manner, the rays converging to/ and falling on H'D, will be reflected 

 parallel to/C, and will intersect the axis of revolution at G, and fall upon the 

 plane FF'. 



If this surface be substituted for the inner reflector DHC (fig. 1G), the rays 

 reflected from the outer mirror whose axis is directed to the sun, when con- 

 verging to/ will meet the inner reflector described by H'QDH, and be reflected 

 (as indicated in fig. 17) so as to intersect its axis of revolution at G, and fall 

 upon the plane FF'. And this is true, whatever angle /G makes with the axis of 

 the exterior reflector. 



Cor. When the number of parts in H'QDRH are indefinitely increased, and 

 their lengths diminished, it evidently becomes the arc of a hyperbola whose 

 foci are/ and G. 



Article 14. The convergence of the solar rays upon a given area can also be 

 effected by combining a number of exterior reflectors, each with its correspond- 

 ing interior, as indicated in fig. 16, the axes of all the exterior parabolic reflectors 

 being directed to the centre of the sun's disc, while the axes of the interior are 

 directed to the centre of the given spot, on which the light has to be cast. 

 Neither is it necessary that the respective reflectors should be complete symme- 

 trical paraboloids: the exterior may consist of a series of large plates, each form- 

 ing a part of a paraboloid of revolution, with a corresponding plate cut from a 

 less paraboloid for its inner reflector. If the axes of all the exterior plates be in 

 the same straight line, such a combination may have a common focus, each 

 interior having that diameter of its generating parabola, which passes through 

 the centre of the plate directed to the spot on which the light is required to fall. 

 The practicability of such a combination is evident, from fig. 16, where K may be 

 viewed as the centre of one of the exterior plates, and H that of its correspond- 

 ing interior, having the diameter of its generating parabola, which passes through 

 II, directed to the plane on which the light is concentrated. The exterior plates 

 may be joined together to move as one piece, and in like manner the interior. 

 This combination is capable of casting the finally reflected beam in a direction 



