The Motion and Distribution of tlie Sun-spots 



19 



the sun-spots. In investigations of the rotation period at dilïerent latitudes, the 

 writers have either hmited the research to recurrent spots, or to such spots as have 

 at least been observed during, say, six consecutive days. 



This method of treatment is naturally sufficient if only averages are to be 

 computed. But if the aim is to get a measure of the disturbing forces or currents 

 in the solar atmosphere this method does not seem sufficient. I have therefore at 

 last resolved to follow each spot day by day. Thus, all spots are included in 

 the first treatment that have been observed on the photographs for at least two 

 consecutive days. There is, however, one limitation. Since the co-ordinates of the 

 spots are not so accurately determined in the neighbourhood of the limb of the 

 sun, I have excluded all spots situated more than 60*^ from the central meridian. 

 It is true that a great number of observations are thus excluded which might be 

 very useful, especially in an investigation of the refraction in the solar atmosphere, 

 but the observations are nevertheless very numerous. 



Before any investigation of the motions could be made, it was necessary to 

 transfer the contents of the Ledgers into a card-catalogue. In this catalogue I 

 have written on each card those measures that might be useful in the investigation, 

 as the number of the spot-groups, the time when the photograph was taken, the 

 longitude and latitude of the spot referred to the above-mentioned system of 

 co-ordinates, rotating in 25.38 days, the distance of the spot or of the spot-group 

 from the central meridian, the area of umbra and of the whole spot, corrected 

 for foreshortening and expressed in millionths of the visible hemisphere. I have, 

 moreover, written on the cards the motions of the spot in longitude and latitude 

 referred to the assumed system of co-ordinates, expressed in minutes of arc per 

 hour. Lastly I have introduced the logarithm of the spot-area for reasons that 

 will be given in another place. 



In order to obtain the motions of the spots in longitude and latitude it was 

 necessary to compute the differences between the longitudes and latitudes on two 

 consecutive days, as well as the difference between the times when the photo- 

 graphs were taken. The differences between the co-ordinates, given in degrees, 

 were afterwards reduced to minutes of arc per hour. This preparatory work alone 

 required a considerable time. Thus it was necessary to compute about 55.000 

 differences and to do 18.000 multiplications in order to obtain these motions in 

 longitude and latitude. 



As the longitudes and latitudes are given with an accurary of 0".! and the 

 motions are nevertheless computed with an accuracy of O'.l per hour, we see from 

 this fact that the motions are given with double accuracy. Supposing however 

 that possibly existing errors in the longitudes and latitudes form a normal distri- 

 bution, the errors in the motions also follow the usual Gaussian law. 



As an example of the cataloguing of the Ledgers we choose the spot-group 

 No. 1833 (Table VI). As the spot during the first two and the last three days 

 has a longitude from the central meridian greater than (30°, we omit these five 



