The Motion and Distribution of tlie Sun-spots 



35 



To obtain results directly comparable with those of Maunder, Spöber and 

 others, it is more convenient to compute in the first place a value of the angular 

 velocity from which T may be obtained directly, instead of computing the rotation- 

 period from the characteristics of the motions in longitude. This value of the 

 angular velocity is evidently not identical with -\- but is dependent on the 

 dispersion, as well as on the skewness and excess. 



If we suppose 



T — the sidereal rotation period of the sun in mean solar days, 

 V= the corresponding angular velocity, expressed in minutes of arc per hour, 

 we have evidently according to (10) 



VT = v^t,, . 



Introducing here the value of T from the equation (14) we obtain for V the expression 

 (18) V 



v„ v^' v^' 



The last four terms in the denominator are at most of the magnitude of -^j^, 



tAïï' respectively. By developing this expression and omitting the terms of the 

 fifth and higher orders, we obtain for V, in using the equations (16) the following 

 expression 



(19) v=v,-{- u, — - + ^:;7^^ + ■ ■ • 



Having thus computed F, the rotation period T is obtained from 



(20) T=^. 



The above expression of V deserves a comment. The first term is nothing 

 but the angular velocity of the system of co-ordinates expressed in minutes of arc 

 per hour, besides which indicates the mean value of the motions in longitude 

 referred to this system. Putting 



is evidently the same as writing 



instead of 



M{i-„ + u) 



\f 0 4- tij 



Compare with this the expression (13). The remaining terms of (19) arise from 

 the moments of the second, third and fourth order, or in other words, from the 

 dispersion, skewness and excess. 



