Pardon these figures! But they form the basis of the reasonings which constitute the groundwork of this article, and it is essential to consider them in order to know on what to rely in discussing the system of Sirius. In comparing these last numbers with those of the preceding ephemeris, we see at the first glance that the angle diminishes more rapidly than had been announced, while the distance has continued to increase since 1870 instead of having attained its maximum on that year, as the orbit of Auwers indicated. It is still further shown by the diagram I have constructed that the arc of the observed orbit crosses the calculated orbit about 1668 and is projected outside of it, pursuing a wholly different curve which must be larger than the orbit traced and less eccentric.
If the observed motion were the mean motion, the revolution of the satellite would be accomplished in a period of about one hundred and sixty-seven years. But the arc passed is yet too small to allow any positive conclusion, and, as the observed perturbations of Sirius demand a period of forty-nine years, Ave are brought to the conclusion that the observed companion continues to accelerate its motion and will be found in the west of Sirius in 1892, or else there is another body causing perturbation nearer Sirius, and moving more rapidly.
We should reserve all conclusions in regard to the existence of these other satellites, as well as all difference of period between the observed orbit and the calculated orbit; but the inevitable conclusion is, that the observed positions do not correspond with those of the ephemeris, and that the orbit thence resulting differs from the calculated orbit.
By the aid of all the observations I have constructed the figure, which shows the movement of the observed planet from 1862 to 1877. The central disk represents Sirius; the four cardinal points are indicated by dotted lines; the proper movement of Sirius in space is marked by the large arrow, whose length corresponds exactly to this movement during ten years (the figure is drawn to the precise scale often millimetres for a second). If the small star discovered in 1862 to the east of Sirius did not belong to it, if it was situated in the depths of space far beyond, it would have remained fixed, and Sirius would have moved from it in the direction indicated by the arrow. But, on the contrary, it belongs to Sirius, accompanies that sun in its progress as the earth accompanies its sun, and turns around it in an elliptic orbit. It has yet traversed, from 1862 to 1877, only the line marked on the figure—a curve not long enough to enable us to calculate the remainder of its orbit. As it is seen, this star is quite small by the side of Sirius, but still larger than Jupiter relatively to our sun. Is it an immense planet, totally opaque and shining only by reflection of the light of Sirius? This is not probable; it must still be self-luminous just as our own earth was during so many ages. It does not correspond exactly to the observed perturbations, a fact which