the Vibration of Light and the Plane of Pulurizaliun. 187 



result seemed to favour the conclusiou that the a;ther vibrated 

 in the plane of polarization. But though it is true that the ex- 

 periments of Holtzmann thus indicated a twisting of the plane 

 of polarization in the opposite direction to that which Stokes, 

 according to his hypothesis, had anticipated, yet on the other 

 hand it must be observed that this twisting was, on the average, 

 actually twice as great as it ought to have been according to the 

 observer's own calculations ; so that it was at all events very bold 

 to regard those experiments as supporting a theory with which 

 they agreed so ill. I, at least, concluded that neither of the two 

 theories could account for the actual results observed, and that 

 it was necessary to subject the phajnomenon of diffraction out of 

 one medium into another to a more accurate examination than 

 it had hitherto undergone; and accordingly, by assuming with 

 Stokes that the fether vibrations are perpendicular to the plane 

 of polarization, 1 found that we are led to formula which agree 

 very well with the experiments of Holtzmann. 



The great work of Stokes on difiFraction has unfortunately not 

 been accessible to me ; but what both he and Holtzmann have 

 to impart concerning the theory in question in communicating 

 their experiments, may be briefly summed up as follows : — The 

 gether-vibrations in a ray of light which falls perpendicularly on 

 a diffraction grating, proceed parallel to the plane of the grating; 

 if therefore the light be diffracted, the vibrations may be divided 

 into such as are perpendicular to the diffracted ray, and such as 

 are parallel to it, — the former alone giving rise to the diffracted 

 light, the latter being wholly without iuiiueuce on the diffrac- 

 tion; from which it follows that the plane of vibration of the 

 diffracted ray is always parallel to the vibrations of the incident 

 i*ay, and, further, that if the vibrations of the incident ray make 

 the angle y with the plane of diffraction {i. e. the plane that 

 contains both the incident and the diffracted ray), while those 

 of the diffracted ray make the angle 7', /3 being the angle of dif- 

 fraction, then 



, tan y 



tan 7'= ' 



cosp 



Whether, however, the longitudinal vibrations are really with- 

 out any effect, deserves more particular investigation. We shall 

 sec directly that they ])roduce an effect even in the case of dif- 

 fraction in a single medium, but that when diffraction takes 

 place in the passage from one medium to another, as in the 

 above-mentioned experiments of Holtzmann, their influence 

 admits of no doubt. I would here advert to the formul;e which 

 Cauchy has adduced for the intensity of rcllected and refracted 

 light. Assuming the two hypotheses, that when an fctlier wave 



