466 ASTROPHYSICS 



by planets. At present, terrestrial observers have not the power to 

 measure such minute variations. As the accuracy attainable im- 

 proves with experience, the proportional number of spectroscopic 

 binaries discovered will undoubtedly be enormously increased. In 

 fact, the star which seems not to be attended by dark companions 

 may be the rare exception. There is the further possibility that the 

 stars attended by massive companions, rather than by small planets, 

 are in a decided majority ; suggesting, at least, that our solar system 

 may prove to be an extreme type of system, rather than a common or 

 average type. 



Observations of stellar motions in the line of sight enable us to 

 solve many other important auxiliary problems. Only one will be re- 

 ferred to here. The determination of stellar distances is exceedingly 

 important, and correspondingly difficult. We know trie fairly accu- 

 rate distances of a dozen stars, and the roughly approximate dis- 

 tances of two or three dozen others. Radial velocity observations, in 

 combination with proper motions, will enable us to determine the 

 average distances of entire classes of stars. Let us consider the stars 

 of the fifth magnitude, of which there are a thousand or more. They 

 travel in practically all directions. A definite relation will exist be- 

 tween their average proper motion and their average radial motion, 

 within a small limit of error. If meridian observations ascertain that 

 the average annual proper motion of these fifth-magnitude stars is 

 0.03 seconds of arc, and spectrographic observations determine that 

 their average speed in the line of sight is thirty-five kilometers per 

 second, it is a simple matter to compute what their average distance 

 must be in order to harmonize the two components. 



A study of 280 observed stars as to the relation existing between 

 visual magnitude and velocity in space led to interesting results. 1 The 

 average speed of 47 stars brighter than the third magnitude is 26 km. ; 

 of 112 stars between the third and fourth magnitude, 32 km.; and of 

 121 stars fainter than the fourth magnitude, 39 km. The progression 

 in these results is very pronounced, and I think we are justified in 

 drawing the important conclusion that, on the average, the faint 

 stars of the system are moving more rapidly than the bright stars. 

 This interesting indication should be confirmed or disproved by the 

 use of a much greater number of stars. 



The proper method of combining radial velocities for statistical 

 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 substan- 

 tially 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 

 1 Astrophysical Journal, xni, 80. 



