500 On the Translatory Motion of the Solar System. 

 the earth's annual motion is equal to 



h cos 5j = Ai cosD 1 sin P sin [O — ^] — sinDj cosPj-, 





where 



- sin Dj = sin 23° 38' cos © 



In this formula © denotes the right ascension of the sun, P 

 and ^ the same magnitudes as before, and /z = 20"-4 the velocity 

 of the earth expressed by the angle it subtends at the centre of a 

 circle whose radius is the velocity of light. The total correction 

 of the angle </>, therefore, will be 



since 



A$ = 24"'9[cos& 1 -f-?2Cos6] 5 

 X = rc/*and40"-8tan©=24"-9. 



If by means of this last formula, and under different assump- 

 tions for the value of n, we calculate the correction for each angle 

 (j> in Table III., and afterwards add these corrections to their 

 respective angles, the resulting values of </> + A<£, subtracted from 

 the assumed true value of 2© 4 , that is to say, from 



will give the following 



<£ = 62°55'41", 



Table IV. 



o — 0. 



*o-(*+A0)- 



n=Q. 



n=h 



n=%. 



»=1. 



+ 3 

 -11 

 -26 



+ 3 

 + 9 

 - 3 



u 

 + 4 

 + 5 

 - 6 



+ 4 

 + 3 



- 7 



+ 7 

 - 2 

 -13 



-19 



+ 2 



- 1 



- 3 



- 9 



-10 

 -18 

 -26 



-17 



- 7 



- 5 



-14 

 -10 

 -10 



-12 

 -10 

 -10 



- 8 

 -12 

 -16 



The sums of the squares of the differences are respectively 

 2267, 462, 419, 427, 719. 



So far as we can conclude from the above observations, the 

 influence of the earth's annual motion appears to be verified ; that 

 of the motion of the solar system is less perceptible. Never- 

 theless it is obvious that if we were to assume that motion to be 

 zero, or to be equal to that of the earth in its orbit, the agree- 

 ment between the observations would be worse than under the 

 assumption that the magnitude of the motion in question is 



