I 
108 Mr. herschel on the 
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the diftance of the ftars in the conjunction and oppof tion will 
then be reprefented by the diagonal of a parallelogram, whereof 
the two femi-parallaxes are the tides ; a general expreffion for 
which will be x ^ + 1 : f° r ^ ars a PP a ~ 
tently defcribe two ellipfes in the heavens, whofe tranfverfe 
axes will be to each other in the ratio of M to m (hg. 8.), and 
A a, 3b, Cc, Dd, will be cotemporary fituations. Now, if 
^'QJ? e drawn parallel to AC, and the parallelogram ^BQ^com- 
pleated, we ihall have bQ= |CA- \ca- |Cc= or femi- 
parallax 90° before or after the fun, and B b may be refolved 
into, or is compounded of, Z’Qjmd bq ; but bq — -iBD — \bd— 
the lemi-parallax in the conjunction or oppofition. We alfo 
have R : S ;:^Q : bq — ^ ; therefore the diftance 3b (orD d)~ 
and by fubftituting the value of p into this ex- 
preffion we obtain \J - — — p x-^-f 1, as above. When the 
1 > 2M m RR 7 
ftars are in the pole of the ecliptic, bq will become equal to 
T - 771 — M 
IQ , and B b will be .7071 P M -- • 
Hitherto we have fuppofed the ftars to be all in one line 
Oabc ; let them now be at fome diftance, fuppofe 5" from 
each other, and let them fir ft be both in the ecliptic. This 
cafe is refolvable into the firft ; for imagine the ftar a, fig. 9. 
to ftand at x 9 and in that fituation the ftars x 9 b, c , will be in 
one line, and their parallax exprefied by - P> But the 
angle aEx may be taken to he equal to aQx ; and as the fore- 
going form gives us the angles vE b, vEf, we are to add aEx, 
or 5" to xEb, and we (hall have ciEb. In general, let the dif- 
tance 
