134 MR JOHN SCOTT ON THE BURNING MIRRORS OF ARCHIMEDES. 



A, resulting from the light reflected from the segment of the paraboloid cut off 

 by the plane of the disc produced, 



= 2{c 2 H'(l - sin /3) + c 2 M'(l + sin (8)} = 4c 2 M' = kl . (4), 



I being the intensity at surface of the sun. 



But c — 107 nearly, therefore the numerical value of this equation 



= 45 79 6 hi' 



nearly, which is a degree of concentration several times that of the most powerful 

 burning glass ever constructed. 



Again putting @ = (in Equation 1), 



4cVcl' 



u = JfsmOcosOdOdp. 



and integrating as in Article 4, Equation 4, 



% = 4c 2 M'sin 2 ; .... (5), 



which gives the intensity at the focus of the light reflected from a segment of a 

 paraboloid, intercepted between the vertex and a plane perpendicular to the 

 axis ; and the intensity produced by a zone, intercepted between two planes 

 perpendicular to the axis, is 



4e%r (sin 2 6 - sin 2 (f) = kl (sin 2 6 - sin 2 6') . . (6). 



Equation 5 shows that the concentration at the focus varies as sin 2 : it is a 

 maximum when 6 = 90°, and is independent of the parameter of the parabola. 

 It may therefore be inferred that a reflector employed to detect the heat of the 

 lunar rays should be as large a segment of a paraboloid as possible ; and the 

 same condition is essential in improving to its utmost limit the space-penetrating 

 power of the reflecting telescope. 



Again, suppose the parabolic mirror to extend to infinity, it can also be shown 

 that the light concentrated at the focus on the other side of the small disc is 

 equal to Ac 2 hi' = kl. What has been proved respecting the intensity at the focus 

 is approximately true for every point on the plane of the small disc not farther 



from F than -¥- , the quantity -J- being the radius of the sun's image reflected 



from the vertex of the paraboloid, and p the parameter of the generating para- 

 bola. Thus, in every position in space, when the axis of a parabolic mirror, 

 whose extent of surface is not less than that cut off by a plane passing through 

 the focus, is directed to the sun, a circle of radiant light and heat is formed equal 

 in intensity to the radiation at the solar surface minus the quantity lost by 

 reflection. 



