270 



S. HTRAYAMA. 



The great discrepancies are apparent at a glance. To "find the 

 corrections to the assumed vaines of Prof. Spürer. I took his valuable 

 observations of sun-spots from 1SG1 to 1884, and selected the spots 

 where motions were pretty regular, since , it is clear that for such a 

 determination the duration of the appearance of the spots should be 

 long, and the proper motion regular and small. The number of 

 groups of selected spots amounted to 933, of which the number of 

 regular spots is great for the time of sun-spot maximum. 



Method of Reduction. 



The formula" obtained bv differentiating the fundamental eola- 

 tions (»iving the heliographic longitude and latitude of a sun-spot are 

 too complex to be used for the reduction of the materials of many 

 observations. I haveadopted instead the method due to Carrington, 

 in which, since the error arising from the assumed position of the 

 pole of the sun is obviously felt chiefly in latitude, and not much in 

 longitude, the variation in latitude only is considered. Consider the 

 celestial sphere, the centre of the sun being the centre of the sphere. 



Let A* be the pole of 

 the ecliptic. 



Let V be the sun's 

 true pole. 



Let V be the sun's 

 assumed pole. 



Let PX=I and P'K=I'. 



Let N' be the assumed node, then 

 the angle N'FS=Û\e computed longitude 

 of the spot from the assumed node— a'. 



Let S be a sun-spot, and PS=8 ; 

 P'S=Ô'. 



