264 



A Short History of Astronomy 



[CH. X. 



FIG. 76. The aberrational ellipse. 



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 direc- 

 tion 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 inter- 

 mediate times it 

 undergoes its least 

 displacement, as at 

 B and B'. The 

 greatest displace- 

 ]A ment s A, or half of 

 A A', which is the 

 same for all stars, 

 is known as the con- 

 stant of aberration, 

 and was fixed by 

 Bradley at between 

 20" and 2o|", the 

 value at present accepted being 20" '4 7. The least displace- 

 ment, 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 u minutes (chapter vin., 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 



