260 Royal Astronomical Society. 



and the half of this is the expression for the real motion in a unit of 

 time, answering to a uniform motion with the velocity at the com- 

 mencement of that unit of time. Take now a century as the unit of 

 time ; the sun's mass as the unit of mass ; the distance divided by 

 sin 1' = 206265 times the mean distance of the earth from the sun 

 as the unit of distance ; then this expression becomes 



=0-00000464 . ^ -(^ - ~\m Sn cos m«. 



Since the motion resulting from the foregoing observations is from 

 ten to fifteen millions of times greater than this, it is necessary, for 

 the explanation of it, by means of the attraction of one mass, — 



1. That either m„ be very great; or, 



2. That r« be small, that is, the attracting mass very near to the 

 disturbed star ; or, 



3. That rj be very small, that is, the attracting mass very near 

 the sun. The smallness of §, the distance of the star in motion from 

 the sun, does not produce this effect, since it can be regarded as a 



factor of 1 — — ,. But, what one mass cannot effect, 



rn 



4. The. joint action of millions of existing stars might produce. 

 On the supposition that the hypothesis (1) is the true one, but 



is not connected with (2) or (3), the change of motion which the 

 observations since 1755 have shown, must have existed during a 

 long space of time with a similar amount and direction ; for the re- 

 lative positions of O, S, S„, change during this time, by the small- 

 ness of the existing motions of the sidereal system, so little, that it 

 does not enter at all into the consideration. The change of motion 

 must also increase proportionally to the square of the time, and 

 much greater values are obtained than are consistent with the num- 

 bers of Hipparchus : I find, for example, that this increase of the 

 present observed change of the motion of Sirius, would alter its right 

 ascension, in 2000 years, by more than three degrees. Indepen- 

 dently of this contradiction of the most ancient observations, there 

 is also very little probability that we should be living precisely at 

 that time when a great proper motion of a fixed star had become 

 changed into a motion in the opposite direction, and again becoming 

 great. 



But it would be yet far less likely that this circumstance should 

 take place in two cases independent of each other. One is justified, 

 then, both by observations and probability, to fall back upon the 

 explanation (1), with the exclusion of (2) and (3). 



Against the explanation (4) the same objections sufficiently hold. 



If (3) were the right supposition, a mass existing so near the sun 

 would produce great irregularity in the motions of the planets, which 

 we do not observe to be the case. 



ITiere remains then the explanation (2) alone. Stars, whose 

 motions, since 1755, have shown remarkable changes, must (if the 

 change cannot be proved to be independent of gravitation) be parts 

 of smaller systems. If we were to regard Sirius and Procyon as 



