MR JOHN SCOTT ON THE BURNING MIRRORS OF ARCHIMEDES. 133 



intensity at P of the light radiating from DC, and reflected at P, is equal to that 

 which would have resulted from the sphere AB ; and the same is true for every 

 increment of the elliptic mirror. Therefore, the total illumination at F, from the 

 luminous surface DCE, is equivalent to that from the small sphere AB. 



From this and the preceding article, we infer that a zone or segment of an 

 elliptic reflector may be used as a pyrometer. For if such a zone, contained between 

 two planes perpendicular to the axis, be placed before an opening in a furnace, 

 the place of the focus / falling within the heated body, the heat reflected to F 

 may be reduced, by diminishing the breadth of the zone, until it can be measured 

 by a Fahrenheit thermometer ; and I, the intensity of the total radiation from 

 any point/ within the furnace, can be determined in degrees of Fahrenheit by 

 Art. 4, Equa. 6. 



Article 6. — Prop. When a Parabolic Reflector lias its axis directed to the centre of the Stm, 

 to find the intensity of the converging Mays which fall on a small Plane Disc at the Focus. 



Let a = angular diameter of the sun, which is about 32', 



c = the distance at which the reflected image of the sun expands into a 



circle equal to unity in diameter, being about 107'4, 

 r = PF (fig. 5), 



T = intensity of the sun's rays at the earth's surface, 

 I = intensity at the surface of the sun, 

 u, k, /3, 0, cf>, and V = the same as in proposition (Art. 4). 



Then xr = area of the circle, which the light reflected at P occupies at F 



perpendicular to PF. 



The intensity of the light reflected from the increment of surface at P on 

 this circle by Art. 1, Equa. 6. 



= r 2 sin 6 dd dp x M' -=- -j-% , 



4c 2 M' . A ... 



= sin 6 dd dip ; 



it 



4c 2 M' 

 and on the small disc at F, = sin 6 do dip cos V. 



IT 



cos V = cos j3 cos d — sin fi sin Q cos ©, 

 4c 2 M' 



4c a M f'P 

 .-. u — / / (cos j8 cos 6 — sin 13 sin S cos <p) sin d dd dtp, (1; 



Integrating as in Article 4, we obtain for the intensity of the light reflected 

 from the corresponding sections of the parobolic mirror 



(?hY (1 - sin &), .... (2). 



and c 2 kT (1 + sin 13), . . . . (3). 



Hence the total intensity at F (fig. 5) on the side of the plane disc towards 



