394 DR. C. CHREE: ANALYSIS OF RESULTS FROM THE KEW MAGNETOGRAPHS 
A reference to Table XL, or fig. 2, shows that the most prominent turning-point in 
the diurnal inequality for D is the maximum about 1 p.m. (or 13 h.). It will he seen 
that this comes near the time of occurrence of the single maximum in the 24-liour 
term, of the second maximum in the 12-hour and 8-hour terms, and of the third 
maximum in the 6-hour term. A similar coincidence i\ ill he found in the case of the 
most prominent turning-points in I, H, and A'. 
Variation throughout the Year {Fourier Series). 
§ 37. Fourier series mav he employed to assist in investigating the variation 
throiio-hout the year of the diurnal range, or the sum of the 24 hourly difterences 
from the mean, m’ the values of the c coefficients in the Fourier series representing 
the diurnal inequalities. A variety of these annual variation series have been 
calculated and the results appear in Table XXX. In the formulae t represents an 
angle increasing at the rate of 30° per month, t = 0 answering to the beginning of 
January. In the calculations, the results from the monthly inequalities have been 
treated as corresponding exactly to the middle of the months, and as separated by 
equal intervals ef time. Neither as.sumption is exactly true. In the selection of the 
5 days a month one of the objects kept in view has been that the mean of the 5 days 
should come near the middle of the month, but in general of course only an approxi¬ 
mation is possible. Again, calendar montbs are unequal in length. Still the mean 
day of a calendar month seldom differs by more than 24 hours from the position it 
would occupy if each month were strictly the twelfth of a year, and unless one is 
dealincr with" a very long series of years, or with observational data of exceptional 
accuracy, very little is likely to be gained by replacing calendar months b\ an\ 
theoreticallv more perfect scheme of days. 
In addition to the Fourier series formulce actually found for the annual variation, 
Table XXX. gives the ratio existing between : 
(i.) Pi, the amplitude of the annual term, and M the mean of the 12 monthly 
values of the quantity considered ; 
(ii.) Vo, the amplitude of the semi-annual term, and M; 
(iii.) The amplitudes Po and Pi. 
The final column in the table gives the mean difference, irrespective of sign, 
between the observed and calculated values of each quantity for the 12 months, 
expressed as a percentage of the mean observed value M. In the table, unit} lepre- 
sents 1' in the case of angles and ly in the case of force components. 
