36 



O. A. Åkesson 



For the numerical use of the equation (19) we observe the following. In 

 designating the mean error of a quantity A by s{A), we get from (19) 



b{V) = B (M(,) |i + + small quantities, 



thus, with sutticient accuracy, 



The calculations now show that 

 in numerical computations the 



TABLE XIV. 

 The angular Velocity at different 



Latitade- 



Filst 





Second Period 





V 





V 





20 



34.808 



11 







176 



35.338 



48 



34.929 





562 



35.701 



373 



35.507 





1081 



35.941 



644 



35.579 





1285 



36.292 



1239 



35.867 



N, 



709 



36.281 



1139 



36.154 





314 



36.590 



267 



36 255 



s. 



391 



36.572 



264 



36.131 





1108 



36.334 



888 



36.347 



Ss 



1367 



36.067 



1181 





S4 



1234 





956 



35.790 





621 



35.511 



445 



35.496 



Se 



274 



35.149 



50 



35 501 



s, 



77 



34.540 



15 





s(F) = s(^J. 



s(tto) > O.'i . This circumstance permits us to omit 



terms of the third and fourth order in (19), which 



only amount to a few units in the 



third decimal. In computing the angular 

 Latitudes. . F & 



velocity of the sun at different latitudes, 



we therefore employ the sufficiently 

 accurate formula 



V=v, + u^ — ^. 



I write a„ as it is a question of the 

 dispersion of ti or AX. Now we have 

 previously computed the dispersion of 

 X or cos ß . Employing the formula 

 (11), we then obtain at last as the 

 expression for V at an arbitrary lati- 

 tude ß 



(20) F=35' .461 + Xysecß— 0.0282O;,'^sec^ß. 



This value of V, introduced into the 

 equation (20), gives the following ex- 

 pression for the sidereal rotation-period 

 of the sun 



(21) 



T= 25''. 380 — 0.7l67a:o sec ß -|- 0.0202(^^2 _|_ g^2| gecSß^ 



In the introduction a paper by the Maunders ^ was mentioned. In this paper, 

 as far as I can see, the authors have been guilty of an inadvertency. From the 

 mean of the motions in longitude they have computed the rotation period directly, 

 without regard to the mean error or the dispersion of tlie motions. As I have 

 shown in the preceding lines, the dispersion of the motions will occur in the 

 expression for the rotation period. The authors not having given this dispersion, 

 but merely the averages, I have not computed the error in the period caused by 

 this omission. 



' Cited on page 10. 



