xxiv.] EMPIRICAL KNOWLEDGE, EXPLANATION, &c. 539 



portion of the rays passing through a circular aperture, 

 the illumination of a point upon a screen behind the aper- 

 ture might be many times multiplied. Yet this paradoxical 

 effect was predicted by Fresnel, and verified both by him- 

 self, and in a careful repetition of the experiment, by Billet. 

 Few persons are aware that in the middle of the shadow 

 of an opaque circular disc is a point of light sensibly as 

 bright as if no disc had been interposed. This startling 

 fact was deduced from Fresnel's theory by Poisson, and 

 was then verified experimentally by Arago. Airy, again, 

 was led by pure theory to predict that Newton's rings 

 would present a modified appearance if produced between 

 a lens of glass and a plate of metal. This effect happened 

 to have been observed fifteen years before by Arago, un- 

 known to Airy. Another prediction of Airy, that there 

 would be a further modification of the rings when made 

 between two substances of very different refractive indices, 

 was verified by subsequent trial with a diamond. A 

 reversal of the rings takes place when the space intervening 

 between the plates is filled with a substance of intermediate 

 refractive power, another phenomenon predicted by theory 

 and verified by experiment. There is hardly a limit to the 

 number of other complicated effects of the interference of 

 rays of light under different circumstances which might be 

 deduced from the mathematical expressions, if it were 

 worth while, or which, being previously observed, can be 

 explained. An interesting case was observed by Herschel 

 and explained by Airy.' 



By a somewhat different effort of scientific foresight, 

 Fresnel discovered that any solid transparent medium 

 might be endowed with the power of double refraction by 

 mere compression. As he attributed the double refracting 

 power of crystals to unequal elasticity in different direc- 

 tions, he inferred that unequal elasticity, if artificially 

 produced, would give similar phenomena. With a power- 

 ful screw and a piece of glass, he then produced not only 

 the colours due to double refraction, but the actual duplica- 

 tion of images. Thus, by a great scientific generalisation, 

 are the remarkable properties of Iceland spar shown to 

 belong to all transparent substances under certain conditions. 2 



1 Airy's Mathematical Tracts, 3rd edit. p. 312. 

 * Young's Works, vol. i. p. 412. 



