corresponding to the position which the star would occupy if aberration did not exist. It is not difficult to see that, wherever a star is situated, the earth's motion is twice a year, at intervals of six months, at right angles to the direction of the star, and that at these times the star receives the greatest possible displacement from its mean position, and is consequently at the ends of the greatest axis of the ellipse which it describes, as at a and a', whereas at intermediate
Fig. 76.—The aberrational ellipse.
times it undergoes its least displacement, as at b and b'. The greatest displacement s a, or half of a a', which is the same for all stars, is known as the constant of aberration, and was fixed by Bradley at between 20" and 2012", the value at present accepted being 20"⋅47. The least displacement, on the other hand, s b, or half of b b', was shewn to depend in a simple way upon the star's distance from the ecliptic, being greatest for stars farthest from the ecliptic.
210. The constant of aberration, which is represented by the angle a c b in fig. 74, depends only on the ratio between a c and a b, which are in turn proportional to the velocities of light and of the earth. Observations of aberration give then the ratio of these two velocities. From Bradley's value of the constant of aberration it follows by an easy calculation that the velocity of light is about 10,000 times that of the earth; Bradley also put this result into the form that light travels from the sun to the earth in 8 minutes 13 seconds. From observations of the eclipses of Jupiter's moons, Roemer and others had estimated the same interval at from 8 to 11 minutes (chapter viii., § 162); and Bradley was thus able to get a satisfactory confirmation of the truth of his discovery. Aberration being once established, the same calculation could be used to give the most accurate
