AN ADDRESS ON ASTROPHYSICS. 317
other sources, would be eliminated from many statistical inquiries by having all parts of the sky represented in the solution.
Errors in the tables of absolute wave-lengths do not enter into radial-velocity results, provided the relative values are correct. In fact we scarcely need to know the wave-lengths at all, for the deter- minations of velocity may be put upon a strictly differential basis, and I incline strongly to the belief that this should be done. Let us con- sider the case very briefly. Rowland's wave-lengths are based upon spectrograms taken with high dispersion and resolving power. Radial- velocity spectrograms are secured with instruments of much lower power. Close solar and laboratory lines, of different intensities, clearly separated on Rowland's plates, are blended on stellar plates. For this and other reasons, the effective wave-lengths on the two classes of plates are different. The difficulty of assigning correct wave-lengths in the case of plates taken with a single-prism spectrograph is even greater: whole groups of separate lines are blended into one apparent line, and lines actually single are very few indeed. It is necessary to use blends, both in the stellar and comparison spectra. Two methods at least are available to eliminate errors in velocity due to errors in assumed wave-lengths. First: At the conclusion of a long series of observations of stars of the same spectral type, the velocity yielded by each line for each star should be tabulated. If one line gives velocities consistently large or consistently small, the conclusion is that its effective wave-length has been wrongly assumed, and we should be justified in changing it arbitrarily. And so on, for each line employed. This involves the assumption that the comparison bright-lines and the corresponding stellar lines have the same wave-lengths; and all the wave-lengths are reduced to one system, true for the particular spectro- graph employed. The method is not entirely free from objection. Second: If the solar spectrum and the comparison spectra are photo- graphed on one and the same plate, under precisely the usual observing conditions, measures of this plate, corrected for the observer's very slight radial velocity with reference to the sun, will form a reduction curve of zero velocity, expressed in terms of micrometer readings. If a spectrogram of star and comparison, made with the same instru- ment and measured in the same manner, is compared with this reduc- tion curve, measure for measure, the speed of the star will be obtained directly, and irrespective of wave-length values; and many other fruit- ful sources of systematic error will be eliminated at the same time. Mr. R. H. Curtiss, of Mount Hamilton, formulated a method on this basis last year, and he has applied it to a specroscopic-binary variable star. The observations were made with a spectrograph whose dis- persion is but one fifth, and whose exposure time for a given star is but one tenth that of the Mills spectrograph. The probable error for a faint star seems to be not more than twice as great as that for a