The Motion and Distribution of the Sun-spots 



(44) ^ 



— 11= ^ (Wj — Wo) , 



,,-„ = - y 



the above equations are piinplified into tlie following, where I have given v 

 and 'V- 



(45) 



in stead ot 





^04- 



N = 









a J = 



^20 



^ ^ NN * 



















' • — 



NN, , 



w,) (î«, — JÎ,,) , 



— 2a J 







N^N, (N, 





. S_, = V 





NN \N 



- 2a/ 



. S, = V 





N^N^ iN^ 







NN \N 





Sa/ . E.. = 



^40 — 3V, 







N,N.\ . 



80/ .E^ = ^ 







N,N, 1 





From these 8 equations, in which I have also expressed the known rnoments in 

 c.i, ay, Sx, Sy, Ex and Ey, the unknown quantities may be determined. 



It is, however, easily seen that such a division is impracticable in the present 

 case. Since E^ and Ey are positive in all zones, it follows that 



N N 



(46) 1-''W>»- 



N, , N, 

 N ^"^^ N ■ 



From the last two equations of (45) it follows that 



This is only possible if any of the quotients ~ and — is smaller than 0,211. 



(47) = + 



W.3 ay ' Ey 



Since 



(m, — m,^] (n^ — n^) 

 has the same sign as iV^,^ or r, it follows that 



