[ 1« ] 



VII. Auroral and Sun-spot Frequencies Contrasted. 

 B>rC. Chkee, ScJD., LL.I)., F.R.S* 



§ 1. 'I^vURIXCt several recent investigations I have had 

 JLJ occasion to contrast the annual variation in years 

 of many and in years of few sun-spots of elements such as 

 the diurnal range o£ the magnetic declination, or the £re- 

 quency of occurrence of magnetic storms. The formula 

 first advanced by Wolf 



R = a + 6S (1) 



as connecting R, the range in the mean diurnal inequality of 

 declination throughout the year, with S the corresponding 

 sun-spot frequency — a and b being constants — can be applied 

 with considerable accuracy to the range in individual months 

 of the year, and to magnetic inclination, horizontal force 

 and vertical force, as well as declination. But taking any 

 one element, a and b are different for the different months of 

 the year, and b/a is in general decidedly larger for winter 

 than for summer. 



Suppose, now, that dashed letters refer to a winter, un- 

 dashed to a summer month, and that suffixes 1 and 2 relate 

 to two years in which sun-spots are respectively many and 

 few. Then for the ratio of the ranges in the summer and 

 the winter month concerned, we have in the year of many 

 sun-spots. 



E 1 /K 1 ' = (, ( /a^l + ^;)-(l + ^ 1 ). 



supposing for simplicity the sun-spot frequency the same 

 for the two months. On the same hypothesis, we have for 

 the corresponding ratio in the year when sun-spots are few, 



R 2 /R 2 ' = (a/a')(l + £s»)-*-(l + jjSA 

 From these two equations we at once deduce 



ffla ajg ,aQ -e-*K^{(^X'*w> 



As already mentioned, observation shows that V \a exceeds 

 b/a, and by hypothesis S x — S 2 is positive, thus 



Ro/R/ > Rj/R/ (2) 



In temperate latitudes, whether sun-spots be many or few, 

 the diurnal range of anv magnetic element is larger in 



* Communicated by the Physical Society : read November 23, 1906. 



