122 VELOCITY OF LIGHT. 



ascronomer royal of England, in 172S. This aberration consists in an apparent 



displacement of the star from its true position by the com- 



f^'s* bined influence of the motion of the earth and the progressive , 



°f ff/ motion of light. If, fur instance, the line MN be taken to 



/ [/ I represent a small portion of the earth's path, and S be a fixed 



pn/9p/i star, then while the earth advances in the direction of the 



u/f I arrow from to 0', 0", &c., if the propagation of light were 



111 I' instantaneous through all distanqes, the star would be seen 



__Mn^/<^si^.j^ in the true direction, OS, O's, 0"s', Sec, the telescope OP 



^M»~—-- remaining parallel to itself as the earth moves, in conse- 



Fig. 10. qixence of the immense distance of the star. Also, allowing 



progressive propagation of light, if the earth were without m.otion, the star would, 

 still appear in its true direction. OS, the telescope OP remainmg stationary; 

 but if we suppose both the earth and light to move, then a ray entering the 

 centre of the tube OP, at the summit, would not be in the centre of the; tube 

 when it reached the lower end, but would be displaced toward the rear by a 

 small space equal to the earth's own motion while the ray is descending the 

 tube. To the observer at O, therefore, the telescope would not ap]:)ear to be truly 

 pointed at the star, but would require to to be leaned forward in the direction 

 OP , until the luminous elements which compose the ray (whatever they may 

 be , should follow accurately the axis of the telescope from top to bottom. The 

 star will accordingly seem to be at S', in advance of its. true position, in the 

 direction of the earth's motion. The amount of this apparent displacement will 

 vary with the angle made by the direction of the earth's movement with the 

 direction of the star. When this angle is zero, that is to say when the earth is 

 mo V mg di. ectly toward or from the star, the displacement is zero ; when the 

 angle is 90 '^, or when the earth's motion is directly across the line drawn to the 

 star, it is maximum. For a star in the plane of the earth's orbit, the aberration 

 is apparently an oscillation in a straight line, the duration of the movement in 

 the allernately opposite directions being six months ; for a star in the pole of the 

 ecliptic, or in a direction at right angles to its plane, the apparent path would be 

 a very small ellipse similar to the earth's orbit. The major axis of this ellipse 

 would measure the maximum amount of aberration on both sides of the true 

 place, and this is found to be equal to 40''.88 ; half of this, or 20".44, is the 

 maximum absolute amount of displacement. 'Jlie direction of a star, therefore, 

 when its aberration is maximum, deviates from its true direction as the diagonal 

 of a rectangle deviates from the side. If, in such a rectangle, the smaller side 

 be made equal to the velocity of the earth, the larger will be the velocity of 

 light, and the angle between the larger side and the diagonal will be 20''. 44. 

 But the earth's velocity per second is known, and is about 18.9 miles; hence the 

 velocity of light is 18.9 Xcot20".44=190, 730 miles, a number less than that 

 before obtained by about one one-hundredth part. 



This coincidence of results is sufficiently remarkable, when we consider the 

 extreme delicacy of such measurements as those by which aberration is de- 

 termined, and also the difficulty of fixing, by observation, the exact instant 

 of the immersion or emersion of one of Jupiter's satellites ; but, these difficulties 

 apart, there is nothing surprising in the agreement, since both depend at last 

 for their absolute values upon our received horizontal parallax of the sun. 



Results very nearly similar, however, have been recently obtained by experi- 

 mental methods founded upon principles entirely different from the foregoing. 

 The first of these methods was devised by Mr. Fizeau, of Paris, and executed 

 by him in the vicinity of that city. Having selected two stations, visible from 



