MR JOHN SCOTT ON THE BURNING MIRRORS OF ARCHIMEDES. 145 



making any angle with the axis of the exterior plates ; and by a readjustment of 

 the inner plates, the distance at which the rays finally meet may be varied at 

 pleasure. 



Article 15. It is stated that the Archimedean burning mirror was hexagonal. 

 Let us consider if the combinations we have been illustrating can be made to 

 conform to that figure. The term hexagonal may have reference either to the 

 appearance of the mirror as a whole, or to the form of each individual reflector. 

 Figs. 14 and 15 will correspond to the former; for if the external and internal 

 conical frustums be each divided into six equal segments, with sufficient space 

 between the segments to admit of free motion, the combination, viewed at a dis- 

 tance, will resemble a hexagonal polygon. Assuming the other meaning to be 

 the correct one, we have only to suppose the form of the parabolic plates, which 

 constitute the exterior and interior reflectors previously explained, to be hexagonal. 

 From this would result two advantages : — they could be so formed that the 

 different six-sided figures would unite together without leaving any interval, and 

 the section of the beam cast by each on the required spot, approximating to a 

 circle, would approach more nearly to the maximum effect with a given section 

 of solar light. 



Article 16. — Prop. As the Expansion of the Sun's image is in proportion to the distance 

 from the Point of Reflection, no greater accuracy is required for the construction of 

 curved surfaces, capable of producing Combustion at distances of 150, 200, and 300 feet, 

 than for those of a focal length of only a few inches. 



The expansion being about 1 foot in diameter for every 108 feet of focal 

 distance, it follows that a reflector is sufficiently accurate for a burning glass, if 

 it can concentrate the rays which fall on each part of its surface from the 

 centre of the sun's disc, within a circular area, whose diameter is the same 

 multiple or part of 1 foot which its focal length is of 108 feet. 



The same principle may be exhibited in another and more definite form. Burn- 

 ing-glasses, which produce at the focus an intensity equal to parabolic ones, may 

 be constructed of plane reflectors arranged as tangent planes to a paraboloid of 

 revolution. 



Since the increment of intensity is area of c i rc i e be ( Art 1} Ec l Lia - 6 ' % 1)> if 

 we take a portion of the surface of the paraboloid subtending an angle at the 

 focus not greater than the sun's disc, the denominator of the foregoing frac- 

 tion may be considered constant ; and the intensity at the focus reflected from 

 such an extent will be 



JcV area of circle DE 



area of circle DE 



= M' 



