in the relative SituatioJi of double Stars, &c. 341 
distance, of double stars, as will be reported ; and, in order to 
make the required principles very clear, I shall give them in a 
few short and numbered sentences, that they may be referred 
to hereafter. 
In Plate VII. Fig. 1, let us call the place of the sun, which 
may also be taken for that of the observer, O. In the centre of 
an orbit or plane N F S P is « Geminorum ; and, if any other 
star is to be examined, we have only to exchange the letter ce 
for that by which such double star is known. This letter is 
always understood to represent the largest of the two stars which 
make up the double star ; and a general expression for its smaller 
companion will be x. N, F, S, P, represent the positions of the 
different parts of the heavens, with respect to «, north, fol- 
lowing, south, and preceding; and the small letters n, f, s, p, 
stand for the same directions with respect to O. x a. P, is the 
angle of position of the two stars x and «, with the parallel 
FP. 
As the motion of an observer affects the relative situation of 
objects, we have three bodies to consider, in our investigation of 
the cause of the changes which will be pointed out; the sun, 
the large star, and the small star, or, as we have shortly called 
them, O, a, x. This admits of three cases : a motion of one of 
the three bodies ; another, of two; and a third, of all the three 
bodies together. We shall now point out the consequences that 
will arise in each of the cases. 
Single Motions. 
No. 1. Motion of x. When « and O are at rest, the motion 
of x may be assumed, so as perfectly to explain any change of 
the distance of the two stars, and of their angle of position, 
mdccciii, Y y 
