Our knowledge of the Thermal Conductivities of Crystals is derived mainly from the experiments of de Senarmont, von Lang, and Jannetaz, who, using the wax melting or analogous methods, have determined the ratios of what may be called the “principal conductivities” and the positions of the axes of conductivity within a number of crystals belonging to the simple systems. According to their experiments the isothermal surfaces about a heated point in a crystal are, in general, ellipsoids, having their axes parallel to the optical axes. In the case of a uniaxal crystal, this ellipsoid becomes a spheroid of revolution about the axis, and is, as a rule, oblate or prolate according as the wave-surface for the extraordinary ray is oblate or prolate. Although this rule has a number of exceptions, it is sufficiently general to render it probable that there may be some relation between the passage of light and of heat through a crystal. The recent determinations of the refractive indices of metals by Kundt have shown that they stand in the same order as conductors of heat, and as to the velocity of propagation of light through them, and this fact brings again into prominence the old determinations with respect to crystals. That the comparison which Kundt has made for the metals cannot be carried to other bodies is at once seen from the fact that the index of refraction of iron differs little from those of glass and several commoner crystals, the conductivities of which are shown to be very small compared to that of iron. A comparison may, however, be possible among transparent bodies themselves, and the following experiments were made with the object of furnishing data for this comparison, the results given by previous observers differing greatly from each other. They have, however, been extended to embrace non-transparent bodies commonly in use in a physical laboratory, and about the conductivity of which we have had a very meagre or absolutely no knowledge. The most important consideration in determining the method to be used is the fact that it is difficult to get large pieces of the crystals to be experimented on. This excludes methods requiring large plates, such as that of Weber and Tuschmid, or large spheres or cubes, such as that of Kirchhoff or Thomson. A method which seemed to present several advantages was the one first suggested by Lodge, and which may be called the “divided bar” method, and after some preliminary experiments had been made to determine its suitability, it was finally adopted. It consists in observing the temperature along a bar heated at one end and cooled at the other, and divided halfway between the two ends by a plane perpendicular to its axis, when (1) the divided ends are together, (2) a disc of the crystal or other body is between.