The motion and Distribution of the Sun-spots 



33 



In our previous study of the longitude motions of the spots we have used 

 the quantity AX cos ß . In determining the rotation period we must employ AX in- 

 stead. Within each zone, 5° broad, we may regard cos ß as a constant. In the 

 preceding pages we have put 



AX cos ß = a; . 



If we now introduce 



TABLE XIII. 

 Characteristics of the Motions in Longitude 

 1886-1909. 



AX=-«/ 



we get 



u = X sec ß . 



Putting the mean of u = Uq , the disper- 

 sion of M = Otj, the skewness = S„ , and 

 the excess = £^„, we get the following 

 formulae for the computation of these 

 quantities 







x„ 









N, a 



id S, 



123<i 



+1.107 



+2 351 



+0.036 



+0.305 



N, 



s. 



3844 



+0.961 



+2.343 



+0.005 



+0.284 



^\ 



Ss 



5072 



+0.797 



+2 3U 



+0 041 



+0.298 



^4 





3915 



+0.508 



+2.445 



— 0.004 



+0.236 



^6 



s. 



2001 



+0.279 



+2.478 



-OlOl 



+0.190 





s. 



548 



— 0.015 



+2.490 



—0.142 



+0.280 





8', 



123 



—0.402 



+2.667 







(11) 



My = Tq sec [: 

 a„ = a.,, sec ß 

 S., = S,; 

 En — E,; 



Thus, if îi indicates the longitude motion of a spot, expressed in minutes of 

 arc per hour, and referred to our system of co-ordinates, we then obtain the 

 corresponding rotation period from the formula 



t — — — 



(12) 



We know the mean of m for a great number of spots and therefore also the mean 

 of + n or M.[v^ + u) . The question then is to compute the mean value of t or 

 M{t) . In the first place we remark that 



900 



(13) 



jf(0 + 



or, expressed in words, if the mean of the motions in longitude is known, we can 

 not, from this value alone, compute the rotation period. To do this, it is necessary 

 also to know the disi)ersion, skewness and excess of the motions. Here the dispersion 

 will have a considerably greater influence than the other two characteristics. 

 From the equation (12) we get 



t = fJl + — 



\ î'o î^o ''o 



Lnnds Universitets Årsskrift. N. F. Afd. 2. Bd 10. 



+ ■ 



