This paper describes a determination of the two optical constants of molten metals, the index of refraction, $\ensuremath{\nu}$, and the index of absorption, $\ensuremath{\kappa}$ from the reflection of polarized light at molten-metal surfaces, placed in an inactive atmosphere.The purpose of this experiment is to throw some light upon the behaviour of free electrons in metals.Method.---The constants, $\ensuremath{\nu}$ and $\ensuremath{\kappa}$, are computed from the phase change $\ensuremath{\Delta}$, and the azimuth change $\ensuremath{\psi}$, of polarized light reflected from the surface of the liquid metal at an angle of incidence $\ensuremath{\varphi}$. A Jamin circle is employed, the azimuth of the analyzer being determined by a bi-field of new design.A furnace for melting the metals is made up by winding a few yards of nichrome wire on a hollow iron cone, thus maintaining a temperature of about 400\ifmmode^\circ\else\textdegree\fi{} C. The whole furnace is operated in a water-cooled container through which a stream of hydrogen is made to flow continuously.The metals employed are bismuth, cadmium, tin, lead and binary alloys of these. As a source of light, three strong rays from a quartz mercury arc are used.Results.---A good optical surface is obtained, free from the scratches and impurities of polishing materials.Values of ${v}^{2}\ensuremath{-}{\ensuremath{\kappa}}^{2}$ and $2\ensuremath{\nu}\ensuremath{\kappa}$, are plotted as functions of the composition (atomic concentration) of each alloy. The parameters of the free electrons are also computed and plotted as functions of the composition of the alloy. These parameters are: (1) the product $N\frac{{e}^{2}}{m}$, where the symbols have the meanings usually given in the electron theory, and (2) the frequency of impact of a free electron with the molecules of the metal.From these optically determined free electron parameters, the electrical resistivities of the pure liquid metals and alloys are computed. In every case the agreement with the known electrical resistivity is within the limits of experimental error. A possible explanation of the disagreement between the values of resistivities for solid metals as computed from optical data and from direct electrical measurement, is suggested.The results seem to indicate that the simple free electron theory of Drude and others is applicable to molten metals.
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