to6 
Mr. herschel on the 
removed to E, we Avail have PE£ = E^O = i'' t and PE/J — VEb 
-aEb—\"\ that is, the ftars a, b , will appear to be i / dif- 
,tant. We alfo have PEc = ErO = 4/', and YEa - PEc = aEc 
= ; that is, the liars a, c , will appear to be diftant, when 
the earth is at E. Now, fince we have ^EP=l", and cEP 
= 4", therefore £EP - cEP = bEc = f " - 4." = 4," ; that is, the 
ftars b, c, will appear to be only 4." removed from each other, 
when the earth is at E. 
From what has been Paid, we may gather the following ge- 
neral expreffion, to denote the parallax that will become vifible 
in the change of diflance between the two ftars, by the re- 
moval of the earth from one extreme of its orbit to the other. 
Let P exprefs the total parallax of a fixed liar of the firff mag- 
nitude, M the magnitude of the largeft of the two liars, m the 
magnitude of the fmallell *, and p the partial parallax to be 
obferved by the change in the dillance of a double liar ; then 
will p 
us P = 
rn 
-M 
Mm 
pM?n 
m 
P ; and p being found by obfervation will give 
M An example or two will explain this fufficiently. 
Suppofe a ftar of the firft magnitude Ihould have a fmall liar 
of the twelfth magnitude near it ; then will the partial parallax 
parallax in y Draconis, if at mod it had amounted to 2", it follows, .that the angle 
OtfE may nearly amount to 4 or 5" for any thing we can conclude to the contrary 
from thofe obfervations. 
* As M and m are here taken to exprefs the relative diftances of the ftars, in 
meafures whereof the diftance of the neareft ftar is taken as unity, thofe who 
think the poftulata on which thefe eftimations are built cannot be granted, may 
ftill ufe the following formulae, if inftead of the magnitudes M, m , they put their 
own eftimations of the relative diftances of the ftars, according to any other 
method whatever they may think it mod eligible to adopt ; for the apparent magni- 
tude of ftars is here only propofed as the moft probable means we have of forming 
any conjectures about their relative diftances. 
7 
we 
