Parallax of the Fixed Stars. 109 
tance of the ftars be d , and let the obferved diftance at E be D ; 
then will D~d+p, and therefore the whole parallax of the 
annual orbit will be exprefled by 
D M m — cl M in 
m — M 
P. 
Suppofe the two ftars now to differ only in latitude, one 
being in the ecliptic, the other, for inftance, 5" north, when 
feen at O. This cafe may alfo be refolved by the former ; for 
imagine the ftars b, c, fig. 7. to be elevated at rectangles above 
the plane of the figure, fo that aOb, or aOcy may make an 
angle of 5" at O: then, inftead of the lines Oabc y E a, E b y 
Ec, EP, imagine them all to be planes at rectangles to the 
figure; and it will appear, that the parallax of the ftars in 
longitude muft be the fame as if the fmall ftar had been with- 
out latitude. And fince the ftars b, c, by the motion of the 
earth from O to E, will not change their latitude, we fhall have 
the following conftru&ion for finding the diftance of the ftars 
ab, ac, at E, and from thence the parallax P. Let the tri- 
angle abj 3 , fig. 10. rep relent the fituation of the ftars ; ab is the 
fubtenfe of 5", that being the angle under which they are 
iuppofed to be feen at O, The quantity b (3 by the former 
theorem is found -r -, — P> which is the partial parallax that 
would have been feen by the earth’s moving from O to E, had 
both ftars been in the ecliptic ; but on account of the difference 
in latitude it will now be reprefented by a[ 3 , the hypothenufe 
of the triangle ab[ 3 : therefore, in general, putting ab — d , and 
a jG = D, we have = P- Hence D being taken by 
obfervation and d , M, and m, given, we obtain the total 
parallax. 
If the fituation of the ftars differs in longitude as well as 
latitude, we may refolve this cafe by the following method. 
Let 
