148 MR JOHN SCOTT ON THE BURNING MIRRORS OF ARCHIMEDES. 



that the centre of the luminous circle reflected by each of the mirrors can bo 

 directed with precision to a given point, which in practice is not attainable, their 

 number, or the size of each, must be somewhat increased, to compensate for 

 defective adjustment. After making such an allowance, it will appear that at 

 distances not exceeding 150 feet, between 1G and 20 plane mirrors, each 2^ by 

 1A feet, may be substituted for the numerous combinations of Buffon, the adjust- 

 ment of which required so much time and trouble. 



What has been shown respecting the power of the solar rays to produce com- 

 bustion after one reflection, can easily be extended to the case in which the light 

 undergoes two reflections, the intensity of the final beam being then reduced to 

 about one-fourth that of the direct solar rays. To compensate for this diminu- 

 tion, the exterior reflectors must have about twice the area of Buffon' s com- 

 bination. Taking, for example, the 128 plane mirrors which kindled combustibles 



at 150 feet, the reflecting surface of the combination is j^ — = 42 f square 



feet, and the sectional area of solar light, which we supposed it to reflect, was 



7 x 6 2 x 128 -I- 144 = 25 square feet nearly. It seems then, that about 80 feet of 



reflecting surface, or an extent capable of reflecting 50 square feet of solar light, 

 will be more than sufficient to inflame such a material as tarred wood, &c, at 

 the distance of 150 feet, after having undergone two reflections, — an extent of 

 surface not too great to be united in one compound mirror, constructed in the 

 manner explained in the foregoing articles. 



Considering the scepticism which has prevailed respecting the Archimedean 

 achievement in the most favourable circumstances, we are the less surprised to 

 find that some recent authors, in quoting the passage from Tzetzes, omit the 

 statement which refers to the burning of the Roman ships in winter. Instead of 

 ignoring these winter attacks, let us examine them in the light which Buffon's 

 experiments supply. That performed with 112 mirrors, at the distance of 138 

 feet, was at 4 o'clock on the afternoon of the 3d April, at which time the altitude 

 of the sun in the sky of Paris would nearly correspond to his meridian altitude 

 at mid- winter in the more southern latitude of Syracuse ; and as the difference 

 between the meridian altitude of the sun at the summer and winter solstice 

 amounts to above 46°, it must be admitted that this additional fact corroborates 

 in a striking manner the evidence already adduced. 



Having now shown how compound burning mirrors can be constructed corre- 

 sponding in every respect to the description which Tzetzes gives of the one 

 invented by Archimedes, and that every statement in the passage is in accord- 

 ance with well-established facts, we conclude that his narrative is no fiction, but, 

 on the contrary, a true account of a real mirror, capable of producing all the 

 effects ascribed to it. While this ancient discovery can be tried, after the lapse 



