VOL. LXXII 



] PHILOSOPHICAL TRANSACTIONS. 22/ 



his micrometer give the declination much better, unless the telescope had borne 

 a power of at least 4 or 500. When the angle of position is but small, such 

 as 3, 4, 5, or 6 degrees, and the distance of the stars not above a few seconds, 

 it is evident that a micrometer must be able to measure lOths of a second at 

 least, to give even a tolerable exactness of position. On the contrary, the posi- 

 tion being measured with such a micrometer as I have constructed for the pur- 

 pose, we may thence deduce the declination, with great confidence, true to a 

 quarter of a 10th of a second for every second of the distance of the stars. 



Mr. Mayer's account of a Geminorum, for instance, gives a difference of 

 0'.7 of time in ar, of 3". 8 in declination, and of I to 6 in magnitude or degree 

 of light of the stars. These quantities reduced to my notation, and compared 

 with my measures of the same star, give 



■£ 1 Distance 9".(>35 from centre to centre f a".\ 06 diameters included. 



g ^Position 23° IV n preceding .5^ 32° 47' n preceding. 



u I ^ I 



§ J Magnitude extremely unequal. (_A little unequal. 



To account for this difference, I ascribe Mr. Mayer's error in distance to his 

 method of measuring by time. The error of position follows always from an 

 observation of the declination taken with the common micrometer, when it is 

 deduced from an erroneous ar. In my measures the distance and position are 

 independent of each other, which I consider as no small advantage of my cross- 

 hair micrometer. The error in the magnitudes of the stars I ascribe to the want 

 of power in Mr. Mayer's telescope, which did not separate the stars far enough 

 for him to judge accurately of their size ; otherwise he would soon have found, 

 that instead of 5, there is hardly so much as 1 single degree of difference in 

 their magnitudes. See; fig. 6 for a representation of those stars with my power 

 of 460. 



I do not mean to depreciate Mr. Mayer's method, the excellence of which is 

 well known ; and with some stars of my 3d, all those of the 4th, 5th, and 6th 

 classes, as well as with those still farther distant, to which he has applied it with 

 admirable skill, and " magno labore, multisque nocturnis vigiliis," as he very 

 justly expresses himself, a better can hardly be wished for; but with stars of the 

 2d class which generally differ no more than 1, 2, or 3 tenths of a second of 

 time in ar, and can never differ more than 4 tenths, the insufficiency of 

 measuring by time is obvious. In regard to the declination, it is also no less 

 evident, that it is much more accurate to take an angle, which may be had true 

 to 2 or 3° at most, than to measure its tangent, which in stars of the 2d class 

 is generally no more than 2, 3, or 4" of a degree, and can never exceed 5. I 

 do not so much as mention the stars of the 1st class : they must certainly, as to 



G G 2 



