The Motion and Distribution of tlie 8an spots 



37 



We shall now from the loDgitude motions of the spots numerically compute 

 tlie angular velocity of the sun at different latitudes. From the values of and 

 a.c in table XT, V has been computed by means of equation (20). The computed 

 values of V are given in table XIV. These values of the angular velocity we shall 

 try to satisfy with a relation of the form 



(22) F = F„ 4- sin ß + F., sin^ß , 



where F^ , F, , and F^ are constants which we shall determine by means of the 

 metliod of least squares. The term Fj sin ß has been introduced because the same 

 northern and southern latitude have not the same angular velocity. For determining 

 Fq, Fj and F„ we have the following equations of condition: 





1886 — 1897 



1898— 



1909 





p 



F 



P 



Ft, + 0.53730 F, + 0.2«869F„ = 



34.808 



1 







F„ + 0.46175 F, + 0.21321 V, = 



35.338 



2 



34.929 



1 



Fo + 0.38268 Fj + 0.14644 1\ = 



85.701 



10 



35.507 





Fo + 0.30071 F, + 0.09043 F^ = 



35.941 



20 



3r)..-.79 



KJ 



Fq + 0.21644 F, + 0.04685 V.^ = 



36.292 



26 



35.867 



20 



Fo + 0.13053 Fl + 0.01701 v., = 



36.281 



10 



36 154 





Fo + 0.04362 F, + 0.00190 T'^, = 



36.590 



5 



36.25.^ 



5 



Fo — 0.04362 F, + 0.00190 Fj = 



36.572 



6 



36.131 



6 



Fo - 0.13053 T^i + 0.01704 F^ = 



36.334 



22 



36.347 



17 



Fo — 0.21644 F, + 0.01685 F„ = 



36.067 



26 



35.885 



20 



F„ — 0.30071 Fl + 0.09043 F, = 



35.828 



22 



35.790 



17 



Fo — 0.38268 T'l -f- 0.14644 F2 = 



35.511 



10 



35.496 



8 



F„ — 0.46175 Fl + 0.21321 F, = 



35.149 





35.501 



1 



Fü — 0.53730 T"i + 0 28869 F„ = 



34 540 









The weights -p have been somewhat rounded in their calculation from the mean 

 errors of F . From these equations of condition, the fo owing systems of normal 

 equations have been obtained. 



[ + 167 F, — 4.1340 Fl + 12.0878 F., = + 253.3590 ; 

 First period : — 4.1340 F„ -)- 12.0878 F^ — 0.5315 F., =— 2.0496; 



I + 12.0878 F^, — 0.5315 F^+ 1.4637 F2 = + 14 8684. 



1+ 133F^— 2.2712F, + 7.4776 F, = + 189.2972 ; 

 Second period : - 2.2712 Fo+ 7.4776 F, — 0.2914 F„ = — 3.7728; 



1+ 7.4776 F,— O.2914F1+ 0.7]09F2 = + 9.1070. 



In solving these equations we obtain at last the following expressions for the 

 angular velocity of the sun as a function of the latitude. 



