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1 6 POPULAR SCIENCE MONTHLY. 



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 com- 

 bine 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 pro- 

 portional 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. 



Eadial velocity observers are concerned as to the part played in 

 the results by pressure in the reversing layers of the stars. The dif- 

 ferential 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 



