558 Prof. A. A. Michelson on Metallic 



In point of fact both causes are effective ; and for semi- 

 transparent substances it is impossible to obtain results which 

 agree even approximately with experiment by either formula. 

 But the rigorous expression of Cauchy, which contains both 

 k nnd i, is so unwieldy to be practically useless. 



The difficulty may be obviated by making use of the empirical 



relation E = E 6 + E&, where E= ■ , , . ; which may be trans- 

 lated to mean that the actual " ellipticity " is made up of 

 two parts which combine additively ; one due to the surface 

 film and the other resulting from absorption. 



If the medium under observation be transparent E^=0, 

 hence E 6 = E. If it be opaque E 6 is small compared with 

 Efr, so that approximately E* = E. 



For semitransparent media it will be necessary to deter- 

 mine the absorption, k, by direct measurement, from which 

 Ea- may be calculated by means of the formula 



L 



sinl(tan 2 l + 2) s 



and E e may then be determined by 



Ee — E — Ejfc. 



In the case of substances like fuchsine and diamond green, 

 in which the medium is almost perfectly transparent for 

 certain colours, we may find E e for this colour ; and if it 

 be correct to assume that E 6 does not vary with the colour, 

 the value of E* = E — E e may be accurately determined 

 for the semi-transparent and the opaque portions of the 

 spectrum. 



A fairly good test is that furnished by selenium. The 

 incidence I corresponding to A = 90° is nearly independent 

 of the colour, being about 71°. 



The value of —p- calculated by the preceding formula is, 

 very nearly, l 



d& 1 . 10 



di E 



Following are the values of — yr , E, E«, and k*. 

 ° ai 



* These last are taken from the results of Professor Wood, Phil, Mag. 



