76 
1)K. C. CllREE: SOME PHENOMENA OF SUNSPOTS AND OF 
The relation refers, it should be noticed, to corresponding data from the year as a 
whole. It may be expressed by the equation 
E, = a(l+mS),.(l) 
where H denotes the range of the diurnal inequality of declination, S the sunspot 
frequency, while a and wr are constants for the particular station concerned. 
In several previous papers* I have dealt with this formula, showing that it applies 
equally to the other magnetic elements, though with different values of a and m, 
and that it may be applied—though with less close agreement between observation 
and calculation—to the individual months of the year, provided in as wmll as ci be 
allotted difPerent values in difiPerent months. The values obtained for in for different 
mamietic elements, and for the same element at different seasons of the year, varied 
largely. At all the European stations considered, m was larger for H (horizontal 
force) than for D (declination), and larger for winter than for summer. 
§ 2. Wolf and Wolfer’s frequency figures are not the only statistics published for 
sunspots. Measurements have been made at Greenwich for many years of the areas 
of the faculse, whole sunspot areas and umbrse both as “ projected,” i.e., as measured 
in photographs, and as “ corrected” for foreshortening. In a paperf published in 1906 
I took all the Greenwich measurements into account when discussing D and H data 
from Falmouth for the magnetically quiet days of the twelve years 1891 to 1902. It 
was found {loc. cit.. Table II., p. 168) that for the twelve years mentioned the 
variations from year to year in the four quantities—^whole spots projected, w^hole 
spots corrected, urnbrse projected and umbrae corrected—-had followed so similar 
a course that it could make little difference which of the four one took to represent 
solar activity in any investigation relating to mean annual values. The corrected 
areas, for instance, for whole spots and umbrm stood very nearly in the ratio of 
6 to 1. 
The variation from year to year in Wolfer’s sunspot frequencies differed distinctly 
Init not largely from that of the Greenwdch spot areas. A considerably greater 
divergence appeared in the case of the Gree 2 iwich measurements of faculm. 
Fornmlm of the type (l) were assumed as existing between the range of the mean 
diurnal inequality for the year in D and H at Falmouth and each in turn of the five 
solar quantities—faculse (corrected areas), umbrse (projected and corrected areas), 
whole spots (corrected areas), and Wolfer’s sunspot frequencies. Values were found 
for the constants a and in in (l) l)y tlie method of least squares, and a comparison 
was made {loc. cit., Tables XVIII. and XIX., pp. 190 and 191) between the observed 
and calculated values of the D and H ranges for the twelve years, in order to see in 
which of the five cases tlie agreement witli observation was closest. 
In both D and H the closest agreement was obtained for AVolfer’s frequencies, 
* ‘ Phil. Trans.,’ A, vol. 202, p. 415; vol. 203, p. 151 ; vol. 208, p. 245, &c. 
t ‘ Camhridge Traii.sactious,’ vol. 20, p. 165. 
