purposes is a question of great importance. The method of least-squares is based upon the assumption that the accidental errors of observation follow a certain law, found by experience to be substantially true. This method is not applicable to the combination of radial velocities, unless radial velocities are distributed in accordance with the law of accidental errors. Do stellar velocities whose values are near zero exist in greatest numbers? Or does some moderate speed predominate? The average speed in space of the 280 stars observed spectrographically is 34 km. When a much greater number of radial velocities is available, the law of distribution must be investigated, and a safe method of combination be developed.
Other practical questions exist as to the proper weights to assign to results of different degrees of accuracy, when it is desired to combine them statistically. The speeds of the brighter second-and third-type stars can be determined well within a kilometer per second, whereas the speeds of first-type stars, containing only broad and hazy lines, may be in error from five to fifteen kilometers. Again, low dispersion spectrography is developing so rapidly that in a few years the speeds of hundreds of the fainter stars will be known within two kilometers. Shall the weights assigned to individual results be proportional to the inverse squares of their probable errors? I think not. The deduced solar motion, for example, should refer to an observed program of stars which shall be representative of the entire sidereal system. It must refer to a star with hazy lines, or to a faint star, as truly as to a bright solar-type star. One poorly determined result for velocity, used alone, should have small weight, but a large number of such determinations should be given considerable weight; proper care being taken to avoid systematic error. Prudence would suggest that separate solutions be made, first for the stars whose spectra admit of accurate measurement, and later for those whose spectra contain hazy lines, or which have been observed with low dispersion. From these a guide as to the relative weights to be assigned to the three or more classes of stars in combination may be found.
Redial velocity observers are concerned as to the part played in the results by pressure in the reversing layers of the stars. The differential effects of pressure are too small to detect in stellar spectra by present means, and there is no known method of eliminating them. We have no recourse but to assume that the stellar lines, neglecting the effect of radial motion, are in identically the same position as the solar lines and the laboratory lines of the elements. Whether the lines in the blue stars are produced under lower pressure than those in the sun, and the lines in the red stars under greater pressure than those in the sun, remains unknown, but this is not impossible. The effect of systematic errors in observed speeds from this source, as well as from
