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3. Finally there remains the determination of the velocity of light by observations of the eclipses of Jupiter's satellites. If the improved photometric methods practised at the Harvard observatory make it possible to observe these with sufficient accuracy, the difference in the results found for the velocity of light when Jupiter is nearest to and farthest from the line of motion will give, not merely the motion of the solar system with reference to the stars, but with reference to the luminiferous æther itself. LIX. On a Method of making the Wave-length of Sodium Light the actual and practical Standard of Length. By Albert A. Michelson and Edward W. Morley*. THE first actual attempt to make the wave-length of sodium light a standard of length was made by Peirce†. This method involves two distinct measurements : first, that of the angular displacement of the image of a slit by a diffraction-grating, and second, that of the distance between the lines of the grating. Both of these are subject to errors due to changes of temperature and to instrumental errors. The results of this work have not as yet been published ; but it is not probable that the degree of accuracy attained is much greater than one part in fifty or a hundred thousand. More recently, Mr. Bell, of the Johns Hopkins University, using Rowland's gratings, has made a determination of the length of the wave of sodium light which is claimed to be accurate to one two hundred thousandth part‡. If this claim is justified, it is probably very near the limit of accuracy of which the method admits. A short time before this, another method was proposed by Macé de Lepinay §. This consists in the calculation of the number of wave-lengths between two surfaces of a cube of quartz. Besides the spectroscopic observations of Talbot’s fringes, the method involves the measurement of the index of refraction and of the density of quartz, and it is not surprising that the degree of accuracy attained was only one in fifty thousand. Several years ago, a method suggested itself which seemed likely to furnish results much more accurate than either of the foregoing, and some preliminary experiments made in * Communicated by the Authors. † ‘Nature,’ xx. p. 99 (1879) ; Amer. Journ. Sci. [3], p. 51 (1879). ‡ “ On the Absolute Wave-lengths of Light,” Amer. Journ. Sci. [3], xxxiii. p. 167 (1887) ; Phil. Mag. [5], xxiii. p. 365. § Comptes Rendus, cii. p. 1153 (1886) ; Journ. de Phys. [2], v. p. 411 (1886). | June have confirmed the anticipation. The apparatus for observing the interference phenomena is the same as that used in the experiments on the relative motion of the earth and the luminiferous æther. Light from the source at s (fig. 1), a sodium-flame, falls on the plane parallel glass a, and is divided, part going to the plane mirror c, and part to the plane mirror b. These two pencils are returned along cae and bae, and the interference of the two is observed in the telescope at e. If the distances ac and ab are made equal, the plane c made parallel with that of the image of b, and the compensating glass d interposed, the interference is at once seen. If the adjustment be exact, the whole field will be dark, since one pencil experiences external reflexion, and the other internal. If now b be moved parallel with itself a measured distance by means of the micrometer-screw, the number of alternations of light and darkness is exactly twice the number of wavelengths in the measured distance ; thus the determination consists absolutely of a measurement of a length and the counting of a number. The degree of accuracy depends on the number of wavelengths which it is possible to count. Fizeau was unable to Figs. 1 and 2. observe interference when the difference of path amounted to 50,000 wave-lengths. It seemed probable that with a smaller density of sodium vapour this number might be increased, and |