ISO 



ï'or the period 1 now found 8.92 years, which coidd, therefore,' 

 retain provisionally the assumed value of 9 years, with which the 

 further calculations had already been made. We have 

 -h, — a cos |x„ + 40" it—t,)\ 



and putting 



we then have 



h, = ^ sin 40° {t -t,) -\- y cos 40° (t-t^) 

 k, = iS' 5m 40 ' ( « - <J + y' cos 40^ {t—t,). 



^= — a sm Xo y = « cos Xo 



^' =r a COS Xo y' = « sin x^. 



I calculated each of the four coefficients independently. In this 

 Newcomb's first series was left out, on account of its smaller accuracy. 

 I found, assuming for t„ 1894.5, from both sets of values A and B 

 obtained by the two methods of calculation, 



A 

 Each series being calculated with its own A. and kc 



/?— — 0".30 y = -j- 0".68 [3' = + 0".60 y' ~ + 0".16 



B 

 The he and kc being calculated by formulae a -{- bi 



^— - 0".29 y = + 0".63 [3' = + 0".G0 y' = + 0".14 



After all the results of calculation B seem to me to be the most 



reliable, but the differences between the two sets are very slight. 



We see further that the relations ^' = y and jii=: — y' are very 



satisfactorily fulfilled and may thus assume according to calculation i?: 



«smxo = + 0".22 

 « cos Xo = + 0".62 

 from which 



X. = 19°.53 

 «= +0".66 • 



The value found for Xn must still undergo a small correction, 

 because the annual variation was not assumed quite correctly; 

 considering that the mean epoch of the observ^ations is about 1886, 

 this correction becomes -|- 2°. 98. 



Finallj^ transferring the zero-epoch to 1900.0 we find for our 

 empirical term 



-f 0"Msin \g ^ 244°.4 + 40°.35 («— 1900.0)|. 



The value now determined for the argument for 1900.0 thus 

 agrees very nearly with that found above. The period of this term 

 differs comparatively little from that of the term Br I; the difference 



