138 



ï then examined the accurate length of the period more clo«elj 

 in the following manner. Proceeding from the form asin{<j-\-i) 

 so that — Ay = « cos x — ^'y = « si7i / 



and from the 2"^^ calculation for h^ and k,., the value for x for each 

 year was found as follows 



1847.8 

 48.9 

 50.1 

 51.2 

 52.4 

 53.5 

 54.6 

 55.8 

 56.9 

 58.1 



303° 



39 



40 



48 



106 



194 



169 



299 



285 



22 



1862.5 

 63.5 

 64.5 

 65.5 

 66.5 

 67.5 

 68.5 

 69.5 

 70.5 

 71.5 

 72.5 

 73.5 

 74.5 



155° 



212 

 257 

 350 

 339 

 350 

 45 

 107 

 124 

 188 

 171 

 224 

 286 



1890.5 

 92.5 

 93.5 

 94.5 

 95.5 

 96.5 

 97.5 

 98.5 

 99.5 



1900.5 



225^ 

 282 

 349 

 314 

 60 

 116 

 170 

 191 

 263 

 317 



These values for x were now united in 7 groups, and the mean 

 results for these groups represented by equations x = Xn -f- »" (^ — 1 900.0) ; 

 the first group received the weight 0.7, the others weiglit 1. 



By solving the 7 equations by least squares I found 



X = 244°.7 + 40°.35 («-1900.0). . 

 The differences Obs. — Calc. are given above. 



