ON “QUIET” DAYS DUEINO THE ELEVEN YEARS 1890 TO 1900, ETC. 
415 
Sun-Spot Formula; Numerical Relationships. 
§ 50. The previous methods of investigation all point to the conclusion that the 
relationship between sun-spot frequency and magnetic phenomena varies considerably 
with the season of the year. To give greater definiteness to the results, 1 have 
assumed provisionally a linear relationship"^^ 
R = a = « {1 -f {h/a) S} 
between the range R of a magnetic element and the sun-spot frequency S, with 
“ a” and “ h ” constants for any one month of the year. I have applied the formula 
to quantities other than ranges, e.g., to the sum of the 24 hourly differences in the 
diurnal inequalities, and to the Fourier coefficients of type c. Various methods have 
also been adopted for calculating a and h. 
The first application was to the range data already employed in calculating 
Tables XXXIII. and XXXIV., and to the corresponding data for I and V. In this 
case the constants were determined from the 11 values of the ranne answermo’ to the 
same month of the year, in the difterent years, by least squares. The results thus 
found for a and h and the corresponding values of h/a are given in Table XL. 
The values of h and hja are multiplied by lO'^' so as to avoid decimals. The unit in 
a is R in the case of D and I, and \y in the case of H and V. 
In addition to the values for the individual months of the year, means are also 
given for the whole year and fiir the three seasons. It should be noticed, however, 
that in this case the “ a or “ h” assigned to a season (or to the year) is not itself 
deduced from a seasonal diurnal inequality, but is simply the arithmetic mean of the 
ffis or 5’s for the individual months of the season (or year); also the value of h/a 
assigned to a season (or year) is derived from tlie mean “ /> ” and the mean “ a” for 
the season (or year). 
The value of “ a ” represents of course the value of the range—or other quantity 
dealt v ith which corresponds to a total absence of sun-spots, h is measui’ed in the 
same units as a. S is simply a number, its values for individual months of the period 
dealt with being given m Table I. ; consequently h/a is also a number, and so inde¬ 
pendent of the paiticiilar units employed m the measiii'ement of force or of angles. 
* See “ Pi'eliminary Note ” for historical references. 
