35 ° Dr. Herschei/s Account of the Changes that have happened 
conclusions I have drawn, when it appears that the deviations 
happen sometimes to be on one side, and sometimes on the other 
side, of the true angle of position. For, since that angle is not a 
thing that will change in the course of a few nights, the excess 
of one measure will serve to correct the defect of another; and 
we are not to think it extraordinary, when stars are so near 
together, and their motion through the field of view (in conse- 
quence of the high magnifying power we are obliged to use) so 
quick, that we should now and then even fall short of that ge- 
neral accuracy which may be had by a careful use of the 
micrometer. 
I shall now enter into an examination of the cause of the 
change in the angle of position of the small star near Castor. 
A revolving star, it is evident, would explain in a most satis- 
factory manner, a continual change in the angle of position, 
without an alteration of the distance. But this, being a circum- 
stance of which we have no precedent, ought not to be admitted 
without the fullest evidence. It will therefore be right to exa- 
mine, whether the related phenomena cannot be satisfactorily 
explained by the proper motions of the stars, or of the sun. 
Single Motions. 
(a) The three bodies we have to consider, are O, a, and x ; 
and, supposing them to be placed as they were observed to be 
in the year 1779; the angle x a. P, in Fig. 1, will be 32 0 47'' 
north preceding. We are at liberty to let the angle P « O be 
what will best answer the purpose. Then, in order to examine 
the various hypotheses that may be formed, according to the 
arrangement of the principles we have given, we shall begin 
with No. 1 ; and, as this admits that all phenomena may be 
