96 REPORT ON PHYSICAL OPTICS. 



bodied in an empirical law, in which the intensity is represented 

 by the ordinate of a rectangular hyperbola, the corresponding 

 abscissa being the sine of incidence. This formula then gives the 

 intensity of the light reflected from crown-glass, and therefore also 

 from the substance examined, at the corresponding incidences. Mr. 

 Potter concludes, in this manner, that the intensity of the light 

 reflected from diamond at a perpendicular incidence is 9-3, and 

 that from glass of antimony 8-2, the intensity of the incident 

 light being represented by 100. The intensities calculated from 

 the refractive indices, by the formulae of Young, Poisson, and 

 Fresnel, are 18-36, and 13'33, respectively. This variance in the 

 results of theory and experiment is undoubtedly beyond the limits 

 of the errors of observation; and, were it otherwise, the partial 

 results obtained by Mr. Potter, in these and other experiments of 

 the same nature, agree too closely to permit us to refer the dis- 

 crepancy to such a source. The principle of the method, however, 

 appears (to say the least) uncertain ; and it cannot but be wished 

 that some of the various photometrical methods recently proposed 

 should be applied to the examination of this interesting question. 



The formulae of Fresnel supply the account of the remarkable 

 phenomenon observed by M. Arago ; namely, that when New- 

 ton's rings are formed between a lens of glass and a metallic re- 

 flector, one of the two images into which they are divided by a 

 double-refracting crystal, whose principal section is parallel or per- 

 pendicular to the plane of reflexion, changes its character as the 

 incidence passes the polarizing angle of the glass ; the colours 

 being the same as in the other image when the incidence is less 

 than the polarizing angle, but complementary to them when it is 

 greater. In fact, when the incident light* is polarized perpen- 

 dicularly to the plane of reflexion, the amplitude of the reflected 

 vibration (which vanishes at the angle whose tangent is equal to 

 the refractive index) changes sign in passing through zero, being 

 negative when the incidence is less than that angle, and positive 

 when it is greater. Consequently, if the wave reflected from the 

 glass, at the central spot, is in complete discordance with that re- 

 flected from the metal in the former case, it will be in complete 

 accordance with it in the latter; and the centre, which before was 

 black, will then be white. For the same reason the whole system 



* The effect is the same whether the light be polarized before or after reflexion. 



