Measurement of Curvature and Refractive Index. 31 



pass the focus, an eye immediately behind the focus will see 

 the mirror filled with light; but if it is gradually moved 

 across while the eye still watches the mirror, the illumination 

 of the latter will appear to die away in the same direction as, 

 or in the opposite direction to, the movement of the edge, or 

 uniformly, according as the edge is between the mirror and 

 the focus, or between the eye and the focus, or at the focus. 

 By this means, and by this means only, can the different 

 radii of curvature of the successive zones of a parabolic 

 mirror whose radius of curvature is twenty times its diameter 

 be accurately measured. The close contact between the para- 

 bola and the circle is due to the fact that it is one of the third 

 order. I think it worth mentioning that the formula given 

 by Dr. Draper in the ' Smithsonian Contributions to Know- 

 ledge,' vol. xiv. (1865), for testing the true parabolic form, 

 gives only half the deviation from the sphere, as was pointed 

 out by a correspondent of the ' English Mechanic ' who signs 

 himself " Orderic Vital," and was confirmed by Mr. E. H. 

 Liveing and myself*. I have gone thus fully into the Fou- 

 cault test, as my method involves the same general principle, 

 viz. making the rays return along the path whence they 

 came. 



Before considering the general case applicable to any kind 

 of lens, I think it best first to show the simplicity of the 

 method in a particular and common case — that of a thin equi- 

 convex lens. Fix an ordinary spectacle-lens in a clip, with its 

 principal plane vertical ; in front of it place a card with a small 

 hole in it ; and illuminate the hole with a candle-flame. It 

 will be found that, when the lens is at a certain distance from 

 the card, there is an inverted image of the hole formed on the 

 card. When this is the case, the light leaving the hole and 

 meeting the front surface of the lens is refracted and meets 

 the back surface normally: most of the light passes through; 

 but a small portion is reflected back along the path whence it 

 came, and is sufficient to produce an image easily visible in 

 the day. This distance of the card from the lens, which is the 

 apparent radius of curvature of the back surface seen through 

 the front surface, is throughout this paper called /. The true 

 focal length F of the same lens may be observed in the usual 

 way; but it is more conveniently found by fixing a plane sur- 

 face of glass behind the lens, when it will be found that 

 another image may be produced when the lens is about twice 

 as far from the card as it was before. Since an image is pro- 

 duced, the light must have returned along the path whence it 

 came, and must therefore have struck the plane surface nor- 

 * English Mechanic, vol. xxxi. pp. 89, 184, 207. 



