The Motion and Distribution of tlie Snn-spots 73 



Thus, if F{x, y) 



is the correlation-l'unction of tlie motions of the sun-spots, (Jharlier puts 

 where f^{x, y) and f.,[x, y) , determined from the relations 



J (^-mi)2+(,/-n.)2 



^^ = ^772^' 



U^-, y) = e 



designate the normal frequency-functions of the two components. The prohlem then 

 is to determine 



iV, , a., , h;., , n.J.. 



When the moments of F{x, y) are known, Chaelier shows how these quantities may 

 be determined. Jt appears that the problem in question leads to numerical com- 



TAI^LE XXXI. 

 Coefficient of Correlation and Line of Symmetry. 



Lali- 

 Zones 













Kr) 















224 



6.5S0 



1.481 



— 0.759 



— 0 243 



0.063 



- Ù 



2..^t;7 



2.588 



1,217 



1.171 





<»35 



G.007 



2,217 



- 0.796 



-0.228 



0 031 



- 10.9 



2.451 



2.4S2 



1.424 



1,369 





1725 



6.355 



1.C33 



— 0.700 



- 0 217 



0.023 



- 8 3 



2 521 



2 541 





1 238 





2524 



5.478 



1 528 



— 0.341 



— 0.118 



0.020 



- 4.9 



2.341 



2 347 



1,236 



1,224 



N„ 



1848 



b. m 



1.623 



— 0.299 



— 0.096 



0.C21 



- 3.9 



2 437 



2.441 



1.274 



1,266 



^, 



581 



5.558 



1.541 



— 0.013 



— 0 004 



0.041 



— 0 2 



2 358 



2 358 



1 241 



1.211 



S, 



655 



5.529 



1.233 



+ 0.432 



+ 0.165 



0.038 



+ 5.7 



2 351 



2,360 



1 110 



1,090 



S, 



1996 



5.063 



1 418 



+ 0,295 



+ 0.110 



0.022 



+ 46 



2 250 



2.255 



1.191 



1.181 



Sa 



2548 



5.885 



1.52 1 



+ 0.523 



+ 0.175 



0.019 



+ 6.7 



2.426 



2.438 



1.235 



1.210 



S, 



2190 



5.682 



1.522 



+ 0.428 



+ 0.145 



0.021 



+ 5.8 



2.384 



2. 3^2 



1 234 



1.216 



s. 



1066 



6.256 



1.700 



+ 0.674 



+ 0.207 



0.C29 



+ 8,2 



2.501 



2 521 



1.304 



1,26G 



s,, 



324 



5.927 



1.989 



+ 1 093 



+ 0.318 



0.050 



+ 14.5 



2435 





1.410 



1 306 



putations considerably more simple than the problem of dividing a given frequency- 

 curve into its two components, which problem, as is shown by Pearson, generally 

 leads to an equation of the ninth degree (The nonic of Peakson). 



It now being a question of the motions of the sun-spots, there is nothing giving 

 countenance to the possibility of dividing the correlation-surfaces into spherical 

 components, since, according to the previous investigations, the dispersions of the longi- 

 tude motions are about double the size of the dispersions of the motions in latitude. 

 A trial with the foimulte developed by Chaelier gave tlie following improbable 



Lunds Universitets Årsskrift. N. F. Afd. 2. Bd 10. 10 



