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SCIENCE
[Vol. LXIH, No. 1635
made for determining the apex and velocity of such a motion. These trial solutions were checked by means of a mechanical parallelogram apparatus, and finally by a partial least-squares solution. It was found that a direction towards a point in the constellation Draco, having the right ascension of 262° (17% hours) and the declination of + 65°, when projected on the plane of the interferometer at all times of the day for the three epochs of observations, would have an azimuth which would vary as shown by the smooth, heavy-line curves of Fig. 3. The azimuth would, how-
Civil Tibie-Hours .. „
in magnitude of the observed effect, being the averages from Fig. 2.
The curves so far considered have been plotted with respect to local civil time for Mount Wilson. If the
Fig. 3
ever, vary equally to the east and to the west of north; that is, the curve should be partly above and partly below the horizontal base line of the figure. As drawn, the curves have been arbitrarily displaced downward (westward) to match the broken line curves which show the actual results of observation, taken from Fig. 1.
If the motion has a direction towards the constellation Draco with a velocity of ten kilometers per second, which remains constant throughout the year, its projection on the plane of the interferometer would vary in magnitude throughout the day, for the three epochs of observations, as shown by the smooth curves in Fig. 4. The broken-line curves show the variation
Fig. 4
direction and magnitude of the motion are constant throughout the year the curves of the variation are more appropriately plotted with respect to sidereal time; in Fig. 5 the curves are so plotted, the heavy line representing the averages of all observations for 1925. There is a remarkable agreement of the curves for the different times of year when plotted against sidereal time; the figure shows that the concordance of the curves for the direction of motion is better than for the magnitude. In Fig. 6 the final averages of Fig. 5 are shown by the broken-line curves, whili the computed effects are shown by the smooth curves. For the azimuth the curves are drawn to a scale of displacement twice that of the preceding figures, the better to bring out the remarkable agreement between the curves.
As far as the observed quantities entering into these two curves are concerned, they are quite independent of each other; and each gives values of the
April 30, 1926]
SCIENCE
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right ascension and declination of the earth’s absolute motion. The right ascension is the sidereal time at which the azimuth (in the simple case) passes from east to west of north; this corresponds to the place where the curve crosses its true axis when passing from a maximum to a minimum. The dotted lines in the lower part of Fig. 6 show that this occurs at 17% hours, which is the right ascension of the apex; or being expressed in degrees it is equal to 262°. The declination of the apex may be determined from the amplitude of the curve taken in connection with the latitude of the observatory; the value thus .obtained is a declination of +65°. The observed velocity of the earth’s motion, projected on the plane of the interferometer, should show a daily variation in magnitude as a result of the rotation of the earth on its axis; this magnitude should drop to its minimum value at a sidereal time which is the right ascension of the apex; and should reach its maximum twelve hours from this time. Considering the latitude of Mount Wilson, 31° 14', and the declination of the apex as just determined from the azimuth of observations, it appears that at the time of maximum the plane of the interferometer makes an angle of less than 8° with the direction of the earth’s motion; thus the projection of the velocity at this time does not differ appreciably from its full value, which is then shown to be equal to ten kilometers per second. The declination of the apex may be determined from the magnitude observa
tions, as well as from those for azimuth, since it determines the ratio of maximum and minimum values of velocity for a given latitude. The agreement of the two right ascensions derived from these independent curves, indicated by dotted lines in Fig. 6, together with an equal concordance of the declinations, is a further very strong confirmation of the argument that the observed effects and the presumed motion are directly related.
Average for/925
A study of the numerical results shows that the probable error in the determination of the azimuth of the effect is ~ 2°, while the probable error of the observed velocity on the supposition of a maximum value of ten kilometers per second is — 0.6 kilometers per second.
The argument that the direction and magnitude of the observed ether drift is independent of local time and is constant with respect to sidereal time implies that the effect of the earth’s orbital motion is imperceptible in the observations. No effect of this orbital motion has been found in these observations of 1925; this is strictly in accordance with the results obtained by Michelson and Morley in 1887 and by Morley and Miller in 1905. In order to account for this fact it is assumed that the constant motion of the earth in space is more than two hundred kilometers per second, but that for some unexplained reason the relative motion of the earth and the ether in the interferometer at Mount Wilson is reduced to ten kilometers per second; under these conditions a component motion equal to the earth’s orbital motion would produce an effect on the resultant which is just below the limit of