( 2 J 3 )- 



until tlie beginning- of tiie year 11)01, which were first discussed. 

 Albrecht's method of' reduction niusi then for subsequent years 

 always conduct to the same "mean pole" and could not give any 

 answer to the (luestion of its secular motion. Only an analysis of 

 the total motion can give a criterium for this qnestion in the con- 

 stancy or otherwise of the co-ordinates of the centre found after 

 subtracting the periodical components. 



From the three yearly ellipses, combined with | aud ïj, I calculated 

 three- series of values of $ -f- .7\ and i^ + //i fi"oni 0.1 to 0.1 year. 

 The first series was used for the period 1890.0—1893.5, the second 

 for 1899.0—1899.9 and the tiiird for 1904.5 and following years. 

 The values for tlie iutcruiediate years were obtained l)y simple 

 interpolation. Subtracting these values from ,/■ and //, 1 obtained a 

 continuous series of values of .c, and v/.,, which served as a first 

 approximation of the second component. This series I divided in two : 



A : 1890.0 to 1899.8 B -. 1899.9 to 1908.0 



and first of all 1 deduced the length of the period from transits 

 through the axes of co-ordinates. I found : 



from A : P, = 1.198 year 

 from B: P., = 1.174 year. 



Provisionally I decided on adopting a general mean value, and 

 computed from A and B together: 



l\ = 1.188 year = 434.1 days. 

 1 examined the shape of the second component for three parts of 

 the whole interval, and found three ellii)ses, which agreed inter se 

 so closely, that there was no objection to taking them together in 

 one mean orbit : 



.6-, = + 0."123 sin i|?., — O."o57 cos if?., 

 _V, = + 0. 061 sin x\i^ 4- 0. 126 cos t|'., 



in which i|% has been counted from 1890.198, and increases yearly 

 with 360°: 1.188 = 303.°03. 



Taking the two periodical terms together, we find : 



,v, — 0."186 sin {xp.^ + 335.°1) ^ 

 ;/, — 0."140 sin {\p, -f 64.°2) 



Practically both amplitudes are ecpiai and the phases differ 90°, 

 so that the second component appeai-s to be a circle with a radius 

 of nearly 0."14. 



The co-ordinates ,c^ aiul //.,, com|)uted from the above foi-mulae, 

 were now used to inv{>stigate the yearly couipoiient in second 

 ai»proxiination. For the present 1 shall only mention the i-esult 1 



