ME JOHN SCOTT ON THE BURNING MIRRORS OF ARCHIMEDES. 143 



AB. Since every cylindrical annulus of rays incident on the exterior mirror 

 forms after reflection from the interior a cylindrical annulus of equal thickness, 

 the intensities must be inversely as the mean radii, the loss from reflection being 

 neglected, or, if taken into account, equal to k 2 times the preceding intensity 

 nearly. 



Article 11. — The preceding annulus of rays may be thrown upon a circular 

 area whose diameter is equal to the breadth of the zone, which forms a section 

 of the annulus. To effect this, we have only so to increase the angle DCB, that 

 the rays may meet the axis at the required distance, as shown in fig. 14. 



In like manner, the parallel rays, from any extent of reflecting surface may 

 be thrown upon the area whose section is F/(fig. 15) by constructing one or both 

 of the conical mirrors of frustums having the required extent of curved surface 

 and the requisite inclination, the same axis being common to all. But when the 

 breadths of the annuli are small compared with the distance of the focus F/from 

 the reflectors, the diameter of the circular area mentioned must be increased by 

 the diameter of the sun's image for that distance. 



Cor. When the number of lines CD, DE, EG, &c. (fig. 15), is indefinitely 

 increased, their lengths being diminished, CDEG becomes part of a parabola. 



Article 12. — Prop. If tivo Parabolic Reflectors have a common Focus, the Solar Bays ivhich 

 are made to converge by reflection from the exterior Mirror will again form a beam of 

 parallel Bays by reflection from the surface of the interior one. 



Let MKN and DHC (fig. 16) be sections of two confocal parabolic reflectors 

 of which AB is the axis of the exterior and CE that of the interior, / being their 

 common focus. 



When AB is directed to a point in the sun's disc, the rays which fall on the 

 exterior mirror parallel to the axis AB, in converging to/, will meet the surface 

 of the interior mirror, and be reflected parallel to its axis /CE, as indicated 

 by the course of the rays SKHF. Thus the solar beam of light which falls on 

 the exterior and larger mirror is again reflected into a beam of parallel rays, and 

 the intensity of the final beam will be greater than that of the incident, as 

 explained in the preceding article. Moreover, since the axis /E of the interior 

 mirror may make any angle with AB the axis of the exterior, the final beam 

 may be thrown in any direction. 



VOL. XXV. PART I. 2 O 



