28 O. A. Åkesson 



The adopted system of co-ordinates having an angular velocity of 3ô'.46i an hour, 

 the velocity of rotation determined from the spots of the zone N.^ during the first 

 period would thus be 



35'. 461 -f 0'.954 = 36'. 416 . 



Since, according to the theory of errors, a third of the observations are outside 

 the limits 



we have consequently about 430 of the 1285 observations > 38'.632 and < 34'. 198, 

 which fact clearly proves the uncertainty of the determinations. 



TABLE XL 



Characteristics of the Motions in Longitude. 



Latitude- 





First Period (1886 



— 1897) 







Second Period (18 



98 — 1909) 





























20 





- 0.250 





- 3.000 







11 



+ 1.545 



+ 2.709 











176 





- 0.108 



- 



- 2.609 



- 0.178 



+ 0.335 



48 



— 0.292 



+ 2.880 









^\ 



5K2 



- 



- 0.404 





- 2.442 



— 0.240 



4- 0.116 



373 



-f 0 227 



+ 2.460 



— 0.210 



+ 0.280 





1081 





- 0.635 





- 2.445 



— 0.092 



+ 0 246 



644 



4- 0.317 



+ 2.631 



+ 0.012 





- 0.150 





1285 





- 0.951 





- 2.217 



+ 0.060 



+ 0.273 



1239 



+ 0.569 



+ 2.447 



— 0.030 





- 0.249 





709 





- 1.015 







4- 0.140 



4- 0.272 



1139 



+ 0.835 



+ 2.279 



— 0.034 





- 0.240 



N, 



314 





- 1.296 





- 2.444 



— 0.126 



-j- 0.178 



267 



+ 0.934 



+ 2.237 



+ 0.092 





- 0,162 



^1 



391 





- 1.285 





- 2.492 



+ 0.082 



+ 0,409 



264 



+ 0.792 



+ 2.091 



+ 0.218 



+ 0.347 





1108 





- 1.001 





- 2.191 



— 0.062 



4- 0,328 



888 



+ 1.032 



+ 2 322 



— 0,031 



+ 0.254 



s. 



1367 





- 0.754 





- 2.366 



+ 0.049 



-j- 0.250 



1181 



+ 0.594 



+ 2.491 



+ 0.020 



+ 0.246 



s. 



1234 





- 0,511 





- 2.,335 



— 0.049 



+ 0,236 



956 



+ 0,491 



+ 2.446 



+ 0.095 



H 



- 0,288 





621 





- 0.246 





- 2.555 



+ 0.014 



-f 0.182 



445 



+ 0.212 



+ 2,424 



— 0.014 



H 



- 0.205 



Se 



274 





- 0.095 





- 2.388 



+ 0.030 



-(- 0,202 



50 



+ 0.260 



+ 2.657 









S, 



77 





- 0.630 





- 2.094 







15 



0.000 



+ 3.386 









The values of are evidently a measure of the size of the currents in the 

 solar atmospliere. If the sun were a rigid body with a certain rotation period and 

 the spots were formations fixedly connected with the sun, Oj; would then be equal 

 to zero, or still better, a measure of the accuracy with which the measurements of 

 the co-ordinates of the spots are made. The values of a would under such circum- 

 stances, for reasons that will be given later on, be considerably less than they are 

 now, and only dependent on errors in the measurements of the photographs. 



The great values of a^, given by the observations, must thus be due to an 

 irregularity in the motions of the spots, caused by currents of some kind or other 

 in the atmosphere of the sun. 



Skewness and Excess. As regards the otlier two characteristics, the sJcetvness 

 Sx and the excess Ex, one does not usually take them into consideration in 

 statistical researches. 



The assumption Sx = Ex = 0, signifies that the distribution of the motions 

 follows the usual Gaussian law of errors. Experience from the apphcations of the 



