432 Prof. Powell on the Theory of the Aberration of Light. 



respectively the side and base ; and let a /3 be respectively the 

 angles which d forms with / and e ; so that we have 

 I _ sin & 



e ~~ sin a"' 



or if a be very small, a —j SU1 &• 



Also let / 2 be the side opposite and parallel to /. 



2. Then conceiving / / 2 to be the successive positions of a 

 telescope moving parallel to itself along with the earth through 

 e, light coming from the top of I to the observer's eye at the 

 bottom, (or, more precisely, from some determinate point as 

 the cross- wire,) relatively to the tube and the observer, will in 

 the same time come down the diagonal d relatively to space, 

 by composition of motions. 



3. If at the same time light from a star come directly in 

 the direction d, this will coincide with the former; it will pass 

 down the telescope as it moves, and the two objects will be 

 referred by the eye to the same direction, and will appear to 

 coincide though really separated by the angle «, which is 

 called the aberration. 



4. Since the same inferences would apply also if another 

 parallelogram be similarly constructed on the same diagonal, 

 in like manner it will be seen that two objects moving with 

 the observer would be referred to the same direction (in which 

 they really are), though seen by light which really moves in 

 the diagonal by composition of motions. 



In this sense the aberration of terrestrial objects is spoken 

 of; though it cannot be determined by terrestrial observations. 



5. In this investigation it is assumed that the light from 

 the star comes in its original rectilinear course, and with the 

 same velocity, equally whether the observer be at rest or in 

 motion. It is also assumed that the velocity of light is that 

 given by independent observations, and comparable in a 

 known ratio with that of the earth in its orbit. 



6. Thus, referring essentially to the light coming with the 

 same velocity from the wire to the eye, it is shown that the 

 aberration is explained by a vera causa ; and from the ex- 

 treme accuracy* with which the amount of aberration thus 

 calculated agrees with that directly observed, it follows that 

 the aberration is completely accounted for, and that there is no 

 residual phenomenon. If there were any, then indeed recourse 



* The mean of the direct observations, including the latest, given in 

 Capt. Smyth's Cycle (ii. 401), is « = 20"43. The result of calculation, 

 taking the velocity of light from observation of Jupiter's satellites at 82 

 min. in traversing the radius of the earth's orbit, gives « = 20""2. 



