Vogel, of Potsdam, in 1889, to set the question at rest. His method of reasoning and proceeding was this:
If the fading out which we see is really due to an eclipse by a dark body, that body must be nearly or quite as large as the star itself, else it could not cut off so much of its light. In this case, it is probably nearly as massive as the star itself, and therefore would affect the motion of the star. Both bodies would, in fact, revolve around their common center of gravity. Therefore, when after the dark body has passed in front of the star, it has made one-fourth of a revolution, which would require about seventeen hours, the star would be moving towards us. Again, seventeen hours before the eclipse, it ought to be moving away from us.
The measurement of six photographs of the spectrum, of which four were taken before the eclipses and two afterward, gives the following results:
After eclipses: "Velocity toward the sun equals 47 km. per second.
These results show that the hypothesis in question is a true one, and afforded the first conclusive evidence of a dark body revolving around a distant star. A study of the law of diminution and recovery of the light during the eclipse, combined with the preceding motions, enabled Vogel to make an approximate estimate of the size of the orbit and of the two bodies. The star itself is somewhat more than a million of miles in diameter; the dark companion a little less. The latter is about the size of our sun. Their distance apart is somewhat more than three millions of miles; the respective masses are about one-half and one-fourth that of the sun. These results, though numerically rather uncertain, are probably near enough to the truth to show us what an interesting system we here have to deal with. We can say with entire certainty that the size and mass of the dark body exceed those of any planet of our system, even Jupiter, several hundred fold.
The period of the star is also subject to variations of a somewhat singular character. These have been attributed by Chandler to a motion of the whole system around a third body, itself invisible. This theory is, however, still to be proved. Quite likely the planet which causes the eclipse is not the only one which revolves around this star. The latter may be the center of a system like our solar system, and the other planets may, by their action, cause changes in the motion of the body that produces the eclipses. The most singular feature of the change is that it seems to have taken place quite rapidly, about 1840. The motion was nearly uniform up to near this date; then it changed, and again remained nearly uniform until 1890. Since then no available observations have been published.