( 48 ) 



4. Yearly motion. 



To the original uh and y's of Albrecht the values according 

 to the 431 daj'-motion were applied, in order to derive from 

 the residuals the yearly motion in 2'"^ approxination. I employed 

 for that purpose however values deviating slightly from those found 

 above as the most probable. For the amplitude I adopted 0". 151, for 

 the period 431.0 and for the epoch 2412439 (or 2408560), which is 

 that found by me from Albrecht's summary only. 



Taking the means of the corresponding values for the different 

 years, I obtained for j; and y 10 mean values, from which periodic 

 formulae, depending only on the sine and cosine of the single angle, 

 were derived, just as had been done in the 1st approximation. 



The results found for the 7 years together deviated but slightly 

 from those which the 1st approximation had given, but I had now 

 also the opportunity of dividing the period into two and of deriving 

 the yearly motion from each half separately. 



This seemed desirable, it being a priori very well possible that 

 this motion, probably caused by meteorological influences, might dif- 

 fer considerably in the different years. 



So I found 



from X from y 



«—261 <— 143 



1890—96 X zzz -\- V' AU cos 2 n 7/ = + 0".067 cos 2 ti 



' 365 •' ^ 365 



i— 252 , <— 126 



1890-92 .r = -4- 0".123co«2;i y = + 0".087 cos 2 n 



^ 365 -^ ^ 365 



< — 269 „ i— 163 



1893—96 .r— + 0".113 cos 2 ;r-——- y = + 0".058 cos 2 ti „^- 



365 ■ 365 



The epochs of maxinrum are expressed here in days from the 

 beginning of the year ; if they are expressed in dates they are : 



«o = Sept. 18 <o = May 23 



Sept. 9 May 6 



Sept. 26 June 12 



By the formula found for the whole of the period the means 

 employed are represented as follows: 



