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of testing their accuracy is to place the surface close to a standard plane and examine the appearance of the Newton’s rings formed in the air film between\tluem. This process when executed with proper care is undoubtedly.'fche mo^ accurate, and, indeed, is the only one possible for producing a standard surface; but it is Attended with a number of inconveniences, among which may be mentioned the use of sodium light, the troublesome reflection from the first surface, the faintness of the fringes when the surface to be tested is metallic and the difficulty of getting rid of dust between the surfaces. All of these inconveniences are avoided by the use of the refractometer. For this purpose the apparatus is placed in a vertical plane, the lower mirror, which would then be horizontal, is replaced, first, by the test plane and then by the surface to be worked. The interference fringes in white light can then be conveniently studied while the surface is being corrected.
Another application of this apparatus, suggested by Professor Morle}', is the measurement of coefficients of expansion. For this purpose a bar is provided with silvered glass mirrors at each end (both facing the same way) and a second bar of the substance to be examined and of the same length is furnished in the same way. These are placed in the refractometer, so that the front mirrors, as well as the rear ones, give interference fringes in white light. The auxiliary bar is kept at zero. The bar to be examined is heated, and the fringes* which pass at the front surface are counted as the bar expands, the fixity of the rear mirror being controlled by the colored fringes at its surface. In this method the bars may be a meter in length, and, therefore, the accuracy of the determination would be proportionally greater than in the celebrated experiments of Fizeau, in which the length was limited to a few millimetres.
Evidently the same disposition will also serve Tor measurements of coefficients of elasticit}', with the evident advantage of studying the elastic properties of the substance in thick rods or bars instead of small wires. This method of investigation is not limited to the determination of changes in length, but is quite as applicable to changes in density and optical properties; particularly to the effect on the velocity of light in solids, liquids and gases due to alterations in temperature, pressure, or magnetic or electrical conditions.
It may be mentioned that a great deal of valuable work has already been accomplished in this direction. I need only cite the
ADDRESS BY ALBERT A. MICHELSON.
very interesting and important experiments of Quincke on the compressibility of liquids; of Jamin on the variation of index of refraction of water and of Ketteler and of Mascart on the index of refraction of gases.
It seems somewhat curious that, while the immense advantage of the refractrometer as an accurate means of measuring indices of refraction has been so fully appreciated, its use should be limited to differential measurements. Thus, while it is easy to measure indices of gases, since the difference in optical path for gas and vacuum is so small, the indices of solids and liquids can only be determined in thin plates, and the accuracy of smell measurements must be limited to that of the estimation of the thickness. Such experiments may furnish the data for very interesting and important conclusions concerning the index of refraction and specially the anomalous dispersion of intensely opaque substances, such as metals and quasi metallic bodies. In such work the advantage of the interference method over the prismatic must be quite apparent; but I hope to show that for all measurements of refraction and dispersion—for solids and liquids as well as for gases—this method promises results which may far surpass those given by the prism.
Suppose a piece of the substance cut in the form of a plane parallel plate. The accuracy, parallelism and distance of the surfaces in wave lengths may be determined exactly as in the case of the proposed standard cubic decimeter. Next the nearest whole number of waves in the solid can be determined either by actual count or perhaps more conveniently by a method described in a previous paper. The residual fractional parts of a wave may also be found as there described, or by direct observation of the interference rings between the two surfaces.
The measurement of the index of refraction of a liquid is even more simple. A vessel is made with plane parallel sides, and the number of waves between the inner surfaces determined, first, when empty and then when filled with liquid.
The ratio of these two numbers will be the index of refraction. It will be noted that the only observations required in this process are the counting of two numbers; and as Professor Mendenhall has aptly remarked, a mistake in counting of a whole number is not an error but a blunder.
A blunder very easy to make, be it noted, in dealing with such large numbers as two or three hundred thousand, but whose chance