PROBLEMS OF ASTROPHYSICS 467 



are near zero exist in greatest numbers? Or does some moderate speed 

 predominate? The average speed in space of the 280 stars observed 

 spec trographic ally 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 

 programme 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. 



Radial 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 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 



