14 Mr. G. G. Stokes 07i the Aberration of Light. 



stance p m being by hypothesis small (two or three radii of the 

 planet suppose), it follows that the angle peg is extremely small, 

 and may be neglected. Hence a planet will appear to be dis- 

 placed from the position which it had v/hen the light left it, 

 just as a star in the same direction is displaced. But besides 

 this, the planet has moved from P while the light has been 

 travelling to E, These two considerations combined lead to 

 the formula for aberration, which is applicable to the planets, 

 as is shown in treatises on astronomy. The same reasoning 

 which applies to a planet will apply equally to the sun, the 

 moon, or a comet. 



To give an idea of the sort of magnitudes neglected in neg- 

 lecting p g, suppose p m equal to the diameter of P, and sup- 

 pose the curvature from p to m uniform. Let r be the radius 

 of P, V its velocity, and R the distance P E. The greatest 

 possible value of the angle between the tangents at p and m is 



1) v r v 



^. In this case we should have /.peg = y^ = y D, D 



being the semidiameter of P as seen from E. Hence the an- 

 gle ^^eg- must be very much greater for the moon than for 

 any other body of the solar system ; for in the case of the 

 planets the value ofv is in no instance double its value for the 

 earth or moon, while their discs are very small compared with 

 that of the moon ; and in the case of the sun, although its disc 

 is about as large as that of the moon, its velocity round the 

 centre of gravity of the solar system is very small. It would 

 indeed be more correct to suppose the sun's centre absolutely 

 at rest, since all our measurements are referred to it, and not 

 to the centre of gravity of the solar system. Taking then the 



V 20" 



case of the moon, and supposing ^ = o ^? D = 15', we 



V IbO 



find that the angle peg is about yyth of a second, an insensi- 

 ble quantity. 



If we suppose the whole solar system to be moving in space 

 with a velocity comparable with that of the earth round the 

 sun, it follows from the linearity of the equations employed, 

 that we may consider this motion separately. It is easy to 

 show, that as far as regards this motion, the sun, moon, and 

 planets will come into the positions in which they are seen 

 just at the instant that the light from them reaches the earth. 

 With respect to the stars also, that part of the aberration 

 which varies with the time of year, the only part which can be 

 observed, will not be affected. If we suppose the aether which 

 fills the portion of space occupied by the solar system to be 

 moving in a current, with a velocity comparable with that of 

 the earth in its orbit, the result will still be the same. For if 



