28 Mr. G. A. Schott. On the [Jan. 18, 



quantity (/i 2 l)/(/* 2 -f l), in which ;t represents the refractive index 

 (if the pressural waves or a quantity of that nature which is to 

 be made nearly equal to unity, cannot on any rigid theory be ac- 

 cepted. Hence neither Green's theory, nor any other rigid elastic 

 solid theory, such as that of Voigt or of K. Pearson, can be made to 

 agree with experiment, if we suppose the ether incompressible. The 

 :ilt( riiative assumption of supposing the ether contractile, will be 

 found to agree with experiment, but there is no means of deciding 

 between it and the electromagnetic theory as regards refraction and 

 reflection. 



These theories lead to the following expressions for the ratio of 

 the intensities and the difference of phase of the components, 

 polarised parallel and perpendicular to the plane of incidence, of the 

 reflected light 



/RJ.\ a _ cos 2 (to-f t'i) . sin to sin t t cos to cos t'i cos (tp-M' 

 \R77/ ~co8 2 (to-i,) + cos 3 (to-i) ~ 



TJ 



cos 4 (to i,) 

 tan ( P L - P l I) 



_ _ E sin 2 ip cos tp _ 

 cos (i ii) cos (to + t'i) (1 + D* cos 2 to) + DE sin* to cos 2 to ' 



where R.L, B// are the amplitudes, />_!., pi I the phase retardations of 

 the components polarised perpendicularly (-L) and parallel (//) to the 

 plane of incidence, the amplitude of each incident component being 

 taken as unity, / , t\ are the angles of incidence and refraction, and 

 A, B, D, E are four constants depending on the refractive indices of 

 the two media and on the constitution of the variable layer and satis- 

 fying the theoretical conditions B = (/*!//) E 1 , and the conditions that 

 when the two media are inverted, that is, /*<,, /*i interchanged, A, B 

 remain unchanged, and ^E change sign. 



The expressions for (RJ./R//) 2 and for tan (/>JL />//) show that the 

 change of difference of phase depends chiefly on E, being also slightly 

 modified by D, and that the alteration in amplitude depends chiefly 

 on B, being only slightly affected by A. The accuracy with which 

 the constants can be experimentally determined is thus very different, 

 being greatest for E, less for B, and least for D and A. 



The values of the four constants are independently calculated for 

 several pairs of media from experiments by Jamin, by Kurz, and by 

 Quincke, using the method of least squares and assuming that the 

 observations are equally exact at all incidences, which is only roughly 

 true. 



The numbers for the ratio intensities and the difference of phase 

 calculated with the values of the constants agree rather better with 



