The Motion and Distribution of the Sun-spots 43 



Before proceeding with this investigation I brought together the corresponding 

 zones in the northern and southern hemispheres during both periods. Thus, for 

 each CO, I have combined iVj and from the first period with and S-^ from 

 the second and so forth. Let us for a moment indicate the values of .ry in these four 

 zones by x^^, x,^, and and the number of observations by , and 

 respectively. Then the values of .Tq and for all these four zones combined are 

 computed from the easily deduced formulae 



nx^^ = n^:z^ -j- )h^x^ -\- n^x^ + n^x^ ; 

 HOx^ = Wj^c^^ -|- n^G^^ -\- n^a^^ -{- , 



n = + "2 + + ^4- 



In the expression for the terms containing the différences between the 

 means are omitted. 



TABLE XIX. 



The Values of F^35 .46l (=A7) for different Spot-sizes. 1886-1909. 





1.00 



1.40 



1.80 



2.20 



260 



3.00 





AF 



n 



A F 



n 



AF 





AF 



H A F 





AF 



N, and S, 



lU 



+(1088 



216 



+0'.884 



299 



+1.156 



374 



+0J04 



166 



+1.262 



18 



+0'.941 





319 



+0.915 



649 



+0.718 



868 



+0.770 



1026 



+0.778 



650 



+0.993 



206 



+0.887 



^'3 ' s. 



480 



+0.162 



809 



+0.769 



996 



+0.620 



1341 



+0.559 



943 



+0.577 



298 



+0.662 



. S, 



381 



+0.214 



670 



+0.180 



842 



+0.591 



1039 



+0.454 



682 



+0.495 



178 



+0.403 



=> S, 



183 



—0,049 



377 



+0.176 



405 



+0.048 



492 



+0.048 



368 



+0.258 



114 



+0.371 





(Î3 



— 1.156 



106 



—0.165 



115 



+O1O6 



133 



—0.126 



69 



+0.222 



34 



+0.447 



The computed values of x^ and a.v I have given in table XVII and XVIII. 

 From table XVIII the previously mentioned fact of the dispersion decreasing with 

 increasing spot-area, is clearly proved. From the values of x^^ and Ox-, given in 

 these tables, I have computed the quantity 



V — 35'. 461 = rr,, sec ß — 0.0282ar^sec^ß', 



in which V as before means the angular velocity at the latitude ß. The results of 

 these calculations are given in table XIX, where the quantity ar-^secß — 0.02825^2 sec^ß 

 is designated by AF. Within each zone the number of observations are also 

 given. If we graphically represent the vahies of A F we see pretty clearly that, on 

 an average, A F is increasing with w . In order to get some idea of the size of 

 this increase, I have within each zone expressed A F as a function of to by means 

 of the linear relation 



A F = a + &(ü . 



(25) 

 where 



