direction changes continuously through the year, at all times being tangential to the orbit. The second component is the cosmical motion of the sun and the solar system. Presumably this is constant in both direction and magnitude but neither the direction nor magnitude is known; the determination of these quantities is the particular object of this experiment. The well-known motion of the solar system towards the constellation Hercules, with a velocity of 19 kilometers per second, is only a relative motion of the sun with regard to the group of nearby stars and it may give no information as to the motion of the group as a whole. In fact, the previous ether-drift experiments have clearly shown that the motion towards Hercules is not a component of the absolute motion of the earth. The rotation of the earth on its axis produces a velocity of less than four-tenths of a kilometer per second in the latitude of observation and is negligible as far as the velocity of absolute motion is concerned; but this rotation has an important effect upon the apparent direction of the motion and is an essential factor in the solution of the problem. However, since the orbital component is continually changing in direction, the general solution is difficult; but by observing the resultant motion when the earth is in different parts of its orbit, a solution by trial is practicable. For this purpose it is necessary to determine the variations in the magnitude and in the direction of the ether-drift effect throughout a period of twenty-four hours and at three or more epochs of the year.
The interferometer continually rotates in a horizontal plane about a vertical axis at the latitude of the observatory. As the earth rotates on its axis, the axis of the interferometer extended may be considered as the generating element of a cone, the apex of which is at the center of the earth. The earth in its orbital motion carries this cone around the orbit, the axis of the cone, the earths axis, always pointing in the same direction in cosmic space. At the same time this system with rotations about three different axes is being translated through space in an unknown manner. It is presumed, further, that the ether-drift interferometer will detect only that single component of the complicated combination of translations and rotations which
at the instant lies in the optical plane of the interferometer; it gives the magnitude and direction of this one component. Fig. 17 shows a globe with a model representing an interferometer attached at a point corresponding to Mount Wilson. The wire extending from the pole of the globe indicates the direction of an assumed
Fig. 17. Models illustrating the diurnal variation in the magnitude and direction of the ether-drift effect.
resultant absolute motion. With the earth in the position shown in the left view, the projection of the motion indicated by the wire, on the plane of the interferometer, passes through the north and south points and has a magnitude less than the full value of the motion. When the earth has turned on its axis to the position shown in the middle view, the projection of the absolute motion in the plane of the interferometer lies to the west of north; as the interferometer rotates on its axis the telescope will detect the maximum component when it points west of north. When the earth has turned to the position shown at the right, the projected component of motion will again be north and south and will have a maximum value, slightly less than the full value. Thus there is a diurnal variation in the observed azimuth of ether-drift. It is evident, further, that the angle which the absolute motion makes with the plane of the interferometer varies throughout the day as the interferometer is carried around on the cone described by its axis. In the illustration, the absolute motion most nearly coincides with the plane of the interferometer in the right view which corresponds to a maximum observed effect; in the left view, the motion is more nearly perpendicular to the plane of the interferometer and the effect is a minimum. It follows that there is a diurnal variation in the magnitude of the effect and this is quite independent of the
Fig. 18. Model for studying the components of ether-drift.
azimuth variation, except insofar as they may be produced by one cause.
The model shown in Fig. 18, was prepared to assist in a study of the ether-drift effect in its astronomical relations. The large circular disk represents the plane of the interferometer which can be rotated around the inclined polar axis, bringing its plane into all the possible diurnal positions, corresponding to the Mount Wilson location. At the center of the disk is mounted a parallelogram whose sides can be made to represent any assumed values for the two components of the absolute motion, while the directions can be set as desired and the corresponding resultant will be reproduced. A small electric lamp is so supported that, as the inter
Fig. 19. Model illustrating the diurnal variation in the azimuth of the ether-drift.
ferometer is rotated around the polar axis and while the parallelogram remains stationary, the lamp casts the shadow of the resultant on the plane of the interferometer, showing how the azimuth of the drift varies with the time of day. The angle which the resultant makes with the plane can be observed and thus the variation in magnitude of the drift for the assumed motion is determined. A probable value for the cosmical component of motion having been selected, a single wire representing the resultant for any epoch is substituted for the parallelogram and the diurnal variations in azimuth and magnitude are studied. Three views of the model, Fig. 19, show how the azimuth swings to the west of north and then to the east, for the motion assumed.
It is evident from these models that the observed ether-drift effect would be very different for different resultant motions, as for different epochs, and that it would vary greatly in different latitudes. The conditions shown correspond approximately to the results here to be considered.
Solution for the absolute motion of the solar system
The point on the celestial sphere towards which the earth is moving because of its absolute motion is called the apex of its motion. This point is defined by its right ascension and declination, as is a star, and the formulae of practical astronomy are directly applicable to its determination from the interferometer observations. The theoretical consideration of the determination of the apex of the motion of the earth has been given in a paper by Professor J. J. Nassau and Professor P. M. Morse, which appeared in the Astrophysical Journal for March, 1927.11
Knowing the latitude of the observatory, φ, and the sidereal time, θ, of the observation, two independent determinations may be obtained for the right ascension, α, and for the declination, δ, of the apex of the earths absolute motion, one determination from the observed velocity, V, and one from the azimuth, A, of the ether-drift effect. The ether-drift effect being a second order effect, periodic in each half turn of the apparatus,
11 J. J. Nassau and P. M. Morse, Astrophys. J. 65, 73 (1927).
