31'1 PHILOSOPHICAL TRANSACTIONS. [aNNO 1728. 



the real and visible place of an object, unless the eye is moving either directly 

 towards or from the object. And in all cases, the sine of the difference be- 

 tween the real and visible place of the object, will be to the sine of the visible 

 inclination of the object to the line in which the eye is moving, as the velocity 

 of the eye to the velocity of light. 



If light moved but 1000 times faster than the eye, and an object, supposed 

 to be at an infinite distance, was really placed perpendicularly over the plain in 

 which the eye is moving, it follows from what has been already said, that the 

 apparent place of such an object will be always inclined to that plain, in an 

 angle of 89° 56^-' ; so that it will constantly appear 3^' from its true place, and 

 seem so much less inclined to the plain, that way towards which the eye tends. 

 That is, if AC is to ab, or ad, as 1000 to 1, the angle abc will be 89° 564-', 

 and ACB = 34-', and bcd = 2acb = 7'. So that according to this supposition, 

 the visible or apparent place of the object, will be altered ^' , if the direction of 

 the eye's motion be at one time contrary to what it is at another. 



If the earth revolve round the sun annually, and the velocity of light were to 

 the velocity of the earth's motion in its orbit, which, may at present be sup- 

 posed a circle, as 1000 to 1 ; then it is easy to conceive, that a star really placed 

 in the very pole of the ecliptic, would, to an eye carried along with the earth, 

 seem to change its place continually ; and, neglecting the small difference on 

 the account of the earth's diurnal revolution on its axis, would seem to describe 

 a circle round that pole, every way 3^-' distant from it. So that its longitude 

 would be varied through all the points of the ecliptic every year; but its latitude 

 would always remain the same. Its right ascension would also change, and its 

 declination, according to the different situation of the sun in respect to the 

 equinoctial points; and its apparent distance from the north pole of the equator, 

 would be 7' less at the autumnal, than at the vernal equinox. 



The greatest alteration of the plaoe of a star in the pole of the ecliptic, or 

 which in effect amounts to the same, the proportion between the velocity of 

 light and the earth's motion in its orbit, being known ; it will not be difficult 

 to find what would be the difference on this account, between the true and ap- 

 parent place of any other star at any time ; and on the contrary, the difference 

 between the true and apparent place being given, the proportion between the 

 velocity of light and the earth's motion in its orbit may be found. 



As Mr. B. only observed the apparent difference of declination of the stars, 

 he takes no further notice in what manner such a cause as here supposed, would 

 occasion an alteration in their apparent places in other respects ; but, supposing 

 the earth to move equally in a circle, it may be gathered from what has been 

 already said, that a star which is neither in the pole nor plane of the ecliptic. 



