174 THE PRINCIPLES OF SCIENCE. 



alone, aided by analogy, could never lead to their dis- 

 covery. To divine these enigmas we must be guided 

 by theoretical ideas founded on a true hypothesis. The 

 theory of luminous vibrations presents this character, and 

 these precious advantages ; for to it we owe the discovery 

 of optical laws the most complicated and most difficult to 

 divine/ 



Physicists who embraced the barren emission theory 

 had nothing but their own native capacity and quickness 

 of observation to rely upon. Fresnel having once seized 

 the conditions of the true undulatory theory, as previously 

 stated by Young, was enabled by the mere manipulation 

 of his mathematical symbols to foresee many of the com- 

 plicated phenomena of light. Who could possibly suppose, 

 or even believe on the ground of mere common sense, that 

 by stopping a large portion of the rays passing through a 

 circular aperture, the illumination of a point upon a 

 screen behind the aperture might be many times multi- 

 plied. Yet this paradoxical effect was predicted by Fresnel, 

 and verified both by himself, and in a careful repetition of 

 the experiment in later years, by Billet. Comparatively 

 few persons even now are aware that in the very middle 

 point of the shadow of an opaque circular disc is a point 

 of light sensibly as bright as if no disc had been inter- 

 posed. 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 pre- 

 dict that Newton's rings would present a modified appear- 

 ance if produced between a lens of glass and a plate of 

 rnetal. This effect happened to have been observed fifteen 

 years before by Arago, unknown to Airy ; but another 

 prediction of Airy, that there would be a further modifica- 

 tion 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 



