VOL. XXXV.] PHILOSOPHICAL TRANSACTIONS. 3|5 



will seem to describe about its true place, a figure insensibly different from an 

 ellipse, whose tranverse axis is at right-angle to the circle of longitude passing 

 through the star's true place, and equal to the diameter of the little circle de- 

 scribed by a star (as before supposed) in the pole of the ecliptic ; and whose 

 conjugate axis is to its transverse, as the sine of the star's latitude to the radius. 

 And allowing that a star by its apparent motion does exactly describe such an 

 ellipse, it will be found, that if a be the angle of position, or the angle at the 

 star made by two great circles drawn from it, through the poles of the ecliptic 

 and equator, and b be another angle, whose tangent is to the tangent of a, as 

 radius to the sine of the latitude of the star ; then b will be equal to the differ- 

 ence of longitude between the sun and the star, when the true and apparent 

 declination of the star are the same. And if the sun's longitude in the ecliptic 

 be reckoned from that point where it is when this happens ; then the difference 

 between the true and apparent declination of the star, on account of the cause 

 now considering, will be always as the sine of the sun's longitude from thence. 

 It will likewise be found, that the greatest difference of declination, that can 

 be between the true and apparent place of the star, will be to the semi-trans- 

 verse axis of the ellipse, or to the semi-diameter of the little circle described by 

 a star in the pole of the ecliptic, as the sine of a to the sine of b. 



If the star have north latitude, the time, when its true and apparent declina- 

 tion are the same, is before the sun comes in conjunction with, or opposition to 

 it, if its longitude be in the first or last quadrant, viz. in the ascending semi- 

 circle of the ecliptic ; and after them, if in the descending semi-circle ; and it 

 will appear nearest to the north pole of the equator, at the time of that 

 maximum, or when the greatest difference between the true and apparent de- 

 clination happens, which precedes the sun's conjunction with the star. 



These particulars being sufficient for the present purpose, it may be time 

 enough to enlarge more on this head, when giving a description of the instru- 

 ments, &c. if that be judged necessary to be done ; and when what is now ad- 

 vanced is allowed of, as something more than a bare hypothesis. 



This being premised, Mr. B. next proceeds to determine, from the observa- 

 tions, what the real proportion is between the velocity of light and the velocity 

 of the earth's annual motion in its orbit ; on supposition that the phaenomena 

 beforementioned depend on the causes here assigned. But first he remarks, 

 that in all the observations hereafter mentioned, he has made no allowance for 

 the change of the star's declination on account of the precession of the equinox, 

 on supposition that the alteration from this cause is proportional to the time, 

 and regular through all the parts of the year : having deduced the real annual 

 s s 2 



