347 
in the relative Situation of double Stars, &c. 
expected, that we see them at their greatest distance. I have 
known it to take up two or three months, before the eye was 
sufficiently acquainted with the object, to judge with the requi- 
site precision. 
Whatever may be the difficulties, or uncertainties, attending 
the method of determining the distance of two close stars by 
an estimation of the apparent diameter, it must however be con- 
fessed, that we have no other way of obtaining the same end 
with so much precision. Our present instance of a Geminorum, 
will show the degree of accuracy of which such estimations are 
capable, and at the same time prove, that the purpose for which 
I shall use the estimated interval between the two stars will be 
sufficiently answered. By an observation of the 10th of May, 
1781, we have the diameter of the largest of the two stars to 
that of the smallest as 6 to 5 ; and, according to several mea- 
sures I have taken with the micrometer, we may admit their 
distance, diameters included, to be five seconds. Then, as the 
vacancy between the two stars is nearly, but not quite, 2 dia- 
meters of the large one, I shall value it at i£. From this we 
calculate, that the diameter of the large star, under the circum- 
stances of our estimation, is nearly 1 ",35 : so that an error of 
one quarter of such a diameter, which is the most we can admit, 
will not exceed o ",34. Nor is it of much consequence, if the 
measure of 5" should not be extremely correct; as a small 
mistake in that quantity will not materially affect the error of 
estimation by the diameter, which, from what has been said, if 
the measure was faulty to a second, would not amount to more 
than one-fifteenth part of it. 
Having thus ascertained that no perceptible change in the 
distance of the stars has taken place, we are now to examine 
