200 PHILOSOPHICAL TRANSACTIONS. [ANNO 1782. 



in magnitude. In a Geminorum the stars, though near enough, do not suffi- 

 ciently differ in magnitude to show any parallax. The stars in the Nebula of 

 Orion, on account of their extreme smallness or distance, are still more im- 

 proper than any; and those of y Virginis are equal in magnitude. 



I do not find that any thing else has been done on the subject. Galileo 

 justly remarks, that such observations ought to be made with the best telescopes, 

 and on this occasion he mentions the power of his own, which enlarged the disc 

 of the sun a thousand times, from which we find it magnified about 32 times ; 

 but we can hardly think his or even Dr. Long's, whose power might probably be 

 60 or 70, sufficient for that purpose. What would Galileo say, if he were told 

 that our present opticians make instruments that enlarge the disc of the sun 

 above 40,000 times ? What would even Cassini say, if he were to view the first 

 star of Aries, which, appeared to him as split in two, through a telescope that 

 will show n Coronae borealis and // Draconis to be double stars ? 



But to proceed, I shall now prove that this method, if stars properly situated, 

 such as I have found, are taken, is free from all the errors occasioned by refrac- 

 tion, nutation, precession of the equinoxes, changes of the obliquity of the 

 ecliptic, and aberration of light; and that the annual parallax, if it even should 

 not exceed the 10th part of a second, may still become visible, and be ascer- 

 tained at least to a much greater degree of approximation than it ever has been 

 done. It will also appear, from the great number of observations I have already- 

 made on several double stars, especially 1 Bootis, that we can now with much 

 greater certainty affirm the annual parallax to be exceedingly small indeed ; and 

 that there is a great probability of succeeding still further in this laborious but 

 delightful research, so as to be able at last to say, not only how much the 

 annual parallax is not, but how much it really is. 



Let there be 2 stars at a distance from each other, not exceeding 5 seconds ; 

 suppose them to be observed at an altitude of 20° ; and let them be so situated 

 with respect to each other, that one of them may be 20°, and the other 20° and 

 5" high : then the whole effect of mean refraction at that altitude, by Dr. Mas- 

 kelyne's excellent tables, will be 2' 35".5 for 20°, and 2' 35 y/ .4888 for '20° 5". 

 The difference is O'.Ol 1 1 . Now, in the first place, we have nothing to do with 

 the refraction itself, since the real altitude of the stars is not in question. In 

 the next place, we also have no concern with the difference of refraction between 

 the two stars, though no more than the .01 1 1th part of a second, because the 

 real distance between the two stars is not required. It follows then, that these 

 observations can only be affected by the difference of the difference; that is, by 

 an alteration in the quantity of refraction occasioned by the change of heat and 

 cold, or weight of the atmosphere, and pointed out to us by the rise and fall of 

 the barometer and thermometer. Let us then see what this difference of the 



