o. A. Åkesson 



From the equations (28) and (30) we obtain 



— ßi = 2 sin v[{i) sin ti^ -j- q cos u^^) cos I [p cos — q sin sin I] . 



Seeing that the spots are approximately situated symmetrically on both sides of 

 the central meridian, sin I will, on an average, be equal to zero. Thus we liave only 



ß., — ßj^ = 2 sin v{p sin -f q cos Uq) cos / . 



Here I varies, on an average, from — (60° — 7°. 2) to -|- (60" — 7°.2). For a certain 

 «0 we thus obtain, designating the mean value of ß^ — ßj by 24?/^, //^ being the lati- 

 tude motion in minutes of arc per hour, 



(31) . p sin -|- g cos = ky^ 



where 



24 



Jc = — — = 110.9 . 



2 sm V . Jf(cos I) 



From equation (31) p and q are to be computed. For the sake of comparison we 

 determine p and q from the motions in the two hemispheres during both periods 

 separately. For determining these quantities we 

 thus obtain four systems of equations with ten 

 equations in each system. As regards the vaines 

 of we observe that ety is notliing but the helio- 

 graphic longitude of the earth reckoned from 

 the ascending node of the sun's equator. Seeing 

 that the inclination between the sun's equator 

 and the ecliptic is only T^lö', we may in com- 

 puting at different times of the year employ 

 directly the longitude of the earth, the correction 



))eing at maximum only tg —y or 0".23, 



Designating the longitude of the sun by 

 O we immediately obtain 



=0— 180 — L. 



For L I liave employed Carrington's value 

 L = 73°40' 1850.0. Since this value is only 

 subjected to small variations on acconnt of the 

 precession, I have during both periods made 

 use of the value of L reduced to 1898.0 or 

 L = 740.3. 



Employing the equation (31) for the computation of p and q, the mean 

 values of sin and cos for the different parts of the year must first be cal- 



TABLE XXVJII. 

 Values of u^, iîf(sinM„) and iV/;cos h^,) at 

 different Times in the Year. 



Timo ill 

 the Year 





Mslu n,) 



M(cos Uq] 



0.00 



27°0 



-f- 0.7017 



+ 0,6884 



0.10 



64,1 



+ 0.9747 



+ 0.1291 



0.20 



100.8 



+ 0.8621 



- 0,4740 



0.30 



136.8 



+ 0.4246 



— 0.8883 



0.40 



172.1 



— 0.1634 



— 0.9711 



0.50 



207.0 



— 0.6897 



- 0.7030 



060 



241.9 



— 0 9081 



— 0.1794 



0.70 



277.1 



— 0.8910 



+ 0.4172 



0.80 



31.S.1 











— 0.4699 



+ 0 8637 

 + 0.9723 



0,90 



349.8 



+ 0.1436 



1.00 



27.0 







