ïlie Motion and Distribution of the Sun-spots 59 



culated. These mean values as well as the values of are given in table XXVIII. 

 The normal equations derived from (31) are of the following form: 

 ^y,^^ I P - sin^Wo -\- sin cos u^^ = X kp^ sin , 



\ 2)- sill »0 cos Uq-\- qï^ cos^?^^^ S %y cos . 

 Here sin n„ and cos signify the means of these functions given in table 

 XXVIII. Since 



Ï sin-M,, = X cos'^Wy = 4.840, 

 Ï sin cos = 0, 



the normal equations will be reduced to 

 ^33^ j 4.840i* = Ï /.y/o sin ti^ , 



\ 4.840r/ = X Iq/^ cos 11^ . 

 In using the values of , given in table XXVII, corrected for the mean of the 

 latitude drift in the hemisphere in question, we obtain the following values for p 

 and q, or what is the same, AL sin / and A/. 



Firtif Period [1886—1897): 



Norfhern Hemisphere : 



ALsin / = + 2'. 75 ± 1'.50 ; 



AL=. 



— 10'. 91 ± 1'.59 ; 



Southern Hemisphere : 



AL sin /= 4 ô'.63 ± 2'. 70 ; 



A/ = 



— U'.oo ± 2'. 70; 



Mean 



ALsin/= + 4'. 14 ± 1'.57 . 



AL = 



— 10'. 96 ± 1'.57 . 





Second Period {1898—1909]: 







Northern Hemisphere : 



AL sin / = + 3'. 56 + 2'. 58 ; 



A7 = 



— 2'. 78 ± 2'. 68 ; 



Southern Hemisphere : 



AL sin 1= ^ O.'öl + 3'. 10 ; 



AL = 



— 0'.37 ± 3'. 10 ; 



Mean 



AL sin L= -f 2'.24 + 2'.02 . 



AL = 



— 1'.58 ± 2'.02 . 



These values differ considerably from each other, an example of the difficulty 

 of accurately determining the position of the sun's axis, Whether the variations in 

 the values of AL sin I are actual or only accidental is rather difficult to deter- 

 mine. It seems, however, as if the variations were accidental, especially as the two 

 hemisplieres during both periods give considerably deviating values. Even the great 

 mean errors seem to indicate the variations to be accidental. As regards AL it 

 seems, however, as if this quantity had been increasing in no small degree from 

 the one period to the other. That this circumstance is not accidental appears from 

 a comparison with the results obtained by Dyson and Maunder, which results are 

 brought together in table XXV, borrowed from their paper. In computing from 

 this table the mean values of AL sin L and AL during the periods 1886 — 1897 and 

 1898 — 1909, without regard to the weights, we obtain 



First Period (1886—1897): AL sin L= + 1'.8 ± V .ß ; AL= — 8'.0 ± 1'.4; 



Second Period [1898—1909): AL sin L = — 1'.2 ± 2'.l ; AL= — 1'.5 ± 2'. 3. 



Thus it really seems as if the angle between the sun's equator and the ecliptic had 

 been somewhat diminishing during the time embraced in the investigation. 



