356 T>r. Herschei/s Account of the Changes that have happened. 
of Sirius, and of many others, should be supposed to arise from a 
motion of the solar system. Now, if they are all equally intitled 
to partake of this motion, we can only admit it in such a direc- 
tion, and of such a velocity, as will satisfy the mean direction 
and velocity of the general proper motions of the stars; and 
place all deviations to the account of a real proper motion in 
each star separately. 
Double Motion. 
(f) In order to explain the phenomena of our double star, 
according to No. 4, by the motion of two bodies, for instance a. 
and x, it will be required that they both should move in given 
directions ; that the velocities of their motions should be in a 
given ratio to each other ; and that this ratio should be com- 
pounded with the ratio of their distances from O ; a supposition 
which must certainly be highly improbable. To show this with 
sufficient evidence, let us admit that, according to the best au- 
thorities, the annual proper motion of Castor is — o",io5 in 
right ascension, and o'', 12 in declination towards the north. 
Then, as the small star, without changing its distance, has moved 
through an angle of 21 0 54', the only difference in the two 
motions of these stars, will be expressed by the extent of the 
chord of that angle. To produce the required effect, it is there- 
fore necessary that the motion of a, which is given, should 
regulate that of the small star, whose relative place at the end 
of 23|- years is also given. Then, as a moves in an angle of 
53 0 31' north preceding, and with a velocity which, being ex- 
pressed by the space it would describe in 23! years, will be 
3", 51, it is required that x shall move in an angle of 29 0 25', 
likewise north preceding, and with a velocity of 3^,02 . The 
