ON STAR STREAMING, 263 
From the facts set forth in what precedes we must, therefore, at once 
conclude that one of our sets must have a real systematic motion in 
respect to the other. 
We can even take one further step. As early as 1843, Bravais has 
shown, in a paper to which sufticient attention has not been paid, that, no 
matter how systematic the motions of any group of stars may be, we 
can determine the motion of the solar system with respect to the centre 
of gravity of that group. ‘Therefore, if for the present we take the 
centre of gravity of all the Bradley stars as a fixed point of reference, 
we can determine the direction of the sun’s motion. As far as I know. 
no extensive determination of the solar apex has as yet been made, 
rigorously on the basis of Bravais’ theory.! But, for reasons into which we 
cannot enter here, the result can hardly differ from the best of our modern 
determinations, made by other methods. This position coincides with 
neither of the two points found just now. 
We thus get a clear indication that we have to do with two star- 
streams, parallel to the lines joining our solar system to the two points 
mentioned. 
That the method is not rigorous, that, therefore, the directions here 
found cannot lay claim to any great accuracy, may be left out of con- 
sideration for the present. But what is important to note is: (1) that 
the directions are only apparent directions ; that is, directions of the 
motion relative to the solar system. (2) That if it be true that two 
directions of motion predominate in the stellar world, then, if we refer 
all our motions to the centre of gravity of the system, these two main 
directions of motion must be in reality diametrically opposite. Some 
reflection must convince you that it must be so, and I will not, therefore, 
stop to demonstrate it. 
For the sake of brevity I will call the points of the sphere towards 
which the star-streams seem to be directed the vertices of the stellar 
motion. 
The apparent vertices were thus provisionally found to lie south 
of a Orionis and yn Sagittarii. Knowing with some approximation the 
velocity of the sun’s motion as compared with the mean velocity of the stars,” 
it is easy to derive from the apparent positions of the vertices their true 
positions, which must lie at diametrically opposite points of the sphere, 
Having once got what I considered to be the clue to the systematic 
divergences in the proper motions, and haying at the same time obtained 
an approximation for the position of the vertices, I have made a more 
rigorous solution of the problem. 
I will not here enter into the details of that solution. In order to 
prevent misconception, however, it will be well to state expressly that the 
existence of two main stream-lines does not imply that the real motions 
of the stars are all exclusively directed to either of the two vertices ; 
there is only a decided preference for these directions. In my solution I, 
have assumed that the frequency of other directions becomes regularly 
smaller as the angle with the main stream becomes greater, according to 
the most simple law of which I could think, which makes the change 
dependent on a single constant. 
I have as yet only tinished a first approximation to the solution. 
The result is that one of the true vertices lies very near to £ Orionis ; 
' Such a determination is now being made by one of my students. 
2 For the mean velocity of the stars see Ast7. Nachr., No. 3487, 
