40 x J x 6 2 





/66\2 



r= i33r 





=9 r 





= 8-571' 





= 8-291' 





= 9-951' 



MR JOHN SCOTT ON THE BURNING MIRRORS OF ARCHIMEDES. 147 



On 23d March, heat produced by 40 glasses at 66 ft. French = 



Do. do. 98 „ 126 ft. 



3d April, 4 p.m., do. 112 „ 138 ft. 



10th April, after 12 noon, do. 128 „ 150 ft. 



10th April, 2-30 p.m., do. 148 „ 150 ft. 



11th April, 2-30 p.m., do. 21 „ 20 ft. = 21 x£F=10-5 I'(by Art,3,Eq.l) 



Do. 2-30 p.m., do. 12 „ 20 ft. = 12 x JI'=6 1'. 



In the first experiment, on the 23d March at noon, tarred beech was ignited 

 with the 40 glasses ; but the mirror not being mounted on a stand, acted at a dis- 

 advantage. On the same day, when 98 glasses ignited a plank smeared with tar 

 and brimstone, the mirror is said to have been still more disadvantageously 

 placed. The experiment on the 3d April was at 4 o'clock p.m., with the mirror 

 mounted, and placed on its stand. The sun being weak, a slight inflammation 

 was produced on a plank covered with threads of wool. 



On the 10th April, with a clear sun, the 128 glasses very suddenly kindled a 

 plank of tarred fir. At half-past 2 o'clock on the same day, the combination of 

 148 glasses was tried on a plank of beech tarred in part, and covered in some 

 places with shreads of wool. The inflammation, which was very sudden, com- 

 menced on those parts of the wood which were uncovered. Beech previously 

 charred was the material ignited with 21 glasses, and little combustible materials 

 were the substances set on fire by 12 glasses, on the 11th April. 



An inspection of the results in the preceding table shows that if k — ^ be 

 correct, wood done over in the manner mentioned can be ignited by a heat 

 varying from eight to nine times that of the direct mid-day rays of the sun 

 at Paris in April, and finely divided combustible substances by a heat consider- 

 ably less, as proved by the experiment with 12 mirrors. But if we assume 

 k = §, which is probably nearer the truth, the heat required to produce the same 

 effect will vary between ten and eleven times the sun's mid-day heat. If the 



number in the right-hand column of the preceding table be multiplied by p 



it gives the minimum number of plane mirrors capable in each case of producing 

 ignition — that is, the number of mirrors which come under Equa. 1, Art. 3. 



Supposing k = \, we find the numbers, for the first five experiments adduced, 

 to be respectively 26*6, 18, 16-58, 17-14, and 19-18. The sizes of these mirrors 

 will, of course, depend on the distance of the focus, and the angle at which they 

 receive the incident light. When the distance is about 108 feet, each of them 

 should have an extent sufficient to reflect a beam of solar light, not less than one 

 foot in diameter, and their dimensions vary in the same ratio for other focal 

 lengths. 



As these minimum combinations have been calculated on the assumption 

 vol. xxv. part i. 2 p 



