Mr Stevenson's Totally Beflecting Mirror. 153 



order, illuminated by Fresnel's great lamp, with a wick 3*6 

 inches in diameter, then, if the internal radius of the mirror 

 be assumed at 24 inches, and if //< = 1-55 for the extreme red 

 rays, we shall find, as formerly, the limiting value of -sj/^to be 

 8° ir 40" = 8°-2 nearly ; from which it follows, since -5- =22, 



that there must be 11 zones and a central conoid. Hence 

 >J/ = 7° 49' 34". From this value of -s^, putting d = 24, and 

 /= 1-8, it will be found from the formulae (1) 



r = 70-624; a = 24-260 ; 6 = - 49-940. 

 If r, a, and b, be calculated by means of the osculating circle 

 to the parabola in the manner already explained, it will be 

 found that 



r = 72-517 ; a = 25639 ; 6 = - 51-278. 

 From this it appears that the values of /-, calculated by the 

 two formula, differ by nearly 1*89 inch, or by about ^^th of 

 the whole length of the radius. The difference of the ordi- 

 nates of the circles at the point A will be found in the same 

 manner as before, to be -0027 inch, from which the per- 

 pendicular distance of the arcs is found to be -0018 inch, 

 a quantity quite within the limits of error in constructing 

 such apparatus. 



Finally, the error in inclination of the osculating circle to 

 the parabola at the point A is 5' 46", from which the lateral 

 aberration of the rays from the point F will be about -16 

 inches, a quantity which may be safely neglected with aflame 

 3-6 inches in diameter. It seems, therefore, from these ex- 

 amples that the approximate formulae will give sufficiently 

 accurate results in the cases most likely to occur in practice. 



It may have already occurred to the reader as a remark- 

 able peculiarity of the totally reflecting mirror, that since 

 the rays at their first incidence and final emergence are per- 

 pendicular to the surface of the glass, they sufi^er no devia- 

 tion by refraction ; and consequently the curvature of the dif- 

 ferent surfaces is totally independent of the refractive power 

 of the glass. It is otherwise, however, with the determina- 

 tion of the greatest admissible breadth of the zones. Here 

 the index of refraction of the glass enters as an element 

 into the calculation ; and the higher the refraction the 

 greater may be the breadth of a zone capable of reflecting 



