VOL. LXX1I.] PHILOSOPHICAL TRANSACTIONS. \QQ 



In general, the method of zenith distances lahours under the following con- 

 siderable difficulties. In the first place, all these distances, though they should 

 not exceed a few degrees, are liable to refractions ; and I hope to be pardoned, 

 says Mr. H. when I say that the real quantities of these refractions, and their 

 differences, are very far from being perfectly known. Secondly, the change of 

 position of the earth's axis arising from nutation, precession of the equinoxes, 

 and other causes, is so far from being completely settled, that it would not be 

 verv easy to say what it exactly is at any given time. In the third place, the 

 aberration of light, though best known of all, may also be liable to some small 

 errors, since the observations from which it was deduced laboured under all the 

 foregoing difficulties. I do not mean to say, that our theories of all these 

 causes of error are defective ; on the contrary, I grant that we are for most 

 astronomical purposes sufficiently furnished with excellent tables to correct our 

 observations from the above-mentioned errors. But when we are on so delicate 

 a point as the parallax of the stars ; when we are investigating angles that may 

 perhaps not amount to a single second, we must endeavour to keep clear of every 

 possibility of being involved in uncertainties ; even the 1 OOth part of a second 

 becomes a quantity to be taken into consideration. 



I shall now deliver the method I have taken, and show that it is free from 

 every error to which the former is liable, and is still capable of every improve- 

 ment the telescope and mechanism of micrometers can furnish. Let oe (fig. I, 

 pi. 4,) be two opposite points of the annual orbit, taken in the same plane with 

 two stars a, k, of unequal magnitudes. Let the angle aob be observed when 

 the earth is at o : and let the angle cie6 be also- observed when the earth is at e. 

 From the difference of these angles, if any should be found, we may calculate 

 the parallax of the stars, according to a theory that will be delivered hereafter. 

 These two stars, for reasons that will soon appear, ought to be as near each 

 other as possible, and also to differ as much in magnitude as we can find them. 



Galileo, I believe, was the first who suggested this method ; but in the 

 manner he mentions it in his 3d dialogue of the Systema Cosmicum, it would 

 be exposed to all the difficulties we have enumerated, and would wish to avoid ; 

 for he does not observe that the two stars should be so near each other as thus to 

 preclude the influence of every cause of error. This method has also been 

 mentioned by other authors ; and we find that Dr. Long observed the double 

 star which is the first of Aries in Ptolemy's catalogue ; that in the head of 

 Castor ; the middle one in the sword of Orion ; and that in the breast of Virgo, 

 with telescopes of 14 and 17 feet, and " was persuaded they would be found 

 always to appear the same." Bat when the theory of parallax snail be explained, 

 it will be seen that every one of these stars are totally improper for the purpose; 

 for the stars of y Arietis are near 10" distant from each other, and are also equal 



