AN ADDRESS ON ASTROPHYSICS. 315 



panions — very minute ones compared with the invisible bodies dis- 

 covered in spectroscopic binaries. It is revolving around the center of 

 mass of itself and its planets and their moons. Its orbit around this 

 center is small, and the orbital speed very slight. The total range of 

 speed is but three one hundredths of a kilometer per second. An 

 observer favorably situated in another system, provided with instru- 

 ments enabling him to measure speeds with absolute accuracy, could 

 detect this variation, and in time say that our sun is attended by 

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

 measure such minute variations. As the accuracy attainable improves 

 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 the fairly accurate 

 distances of a dozen stars, and the roughly approximate distances of two 

 or three dozen others. Eadial 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 magni- 

 tude, of which there are a thousand or more. They travel in practically 

 all directions. A definite relation will exist between 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. The 

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

 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 



