panions—very minute ones compared with the invisible bodies discovered 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 instruments 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 referred 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. 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 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 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
