232 
DR. C. CHREE: MAGNETIC DECLINATION 
Table XIX. is principally intended to bring out two facts : (1) that the hour of 
most frequent occurrence of the daily maximum is earlier in years of sunspot 
minimum than in years of maximum ; (2) that the distribution of maxima is more 
concentrated, i.e. less uniform throughout the 24 hours, in years of sunspot minimum 
than in years of maximum. The phenomenon first mentioned is most conspicuous in 
winter. As regards the second phenomenon, there is an apparent exception in 
winter, the occurrences between midnight and 10 a.m. then diminishing slightly with 
increased sunspot frequency. This diminution is, however, more than made up for 
by the increase in the occurrences between 4 p.m. and midnight, and it probably 
merely represents the tendency to a closer approach to equality between the morning 
and evening occurrences which is seen in sunspot maximum years at the other 
seasons. 
In the case of the daily minima, the differences between the phenomena in years of 
sunspot maximum and minimum are small. Table XX. does, however, show that in 
winter and equinox there is, in the years of sunspot maximum, a reduction in the 
disproportion of the evening and morning occurrences. 
Annual Variation. Fourier Coefficients. 
§ 24. The mean monthly values of an element during the year may be analysed in 
a Fourier series 
M + Pj sin (t + O i) + P 2 sin (2 1 + 0 2 )+ ..., 
where t denotes time counted from January 1st, 30° being taken as the equivalent 
of one month. M denotes the arithmetic mean of the 12 monthly values, Pj and P 2 
the amplitudes of the annual and 6-month terms, while 6 X and 0 2 represent the phase 
angles. One month of time answers, of course, to 30° in 9 X , to 60° in 9 2 , and so on. 
In determining the constants the observed monthly values were treated as if 
separated by exactly equal intervals of time. This is not strictly true, and there is a 
corresponding slight uncertainty in the results. Practically the same uncertainty 
enters, however, into the several groups of years and the different species of days, 
and the principal object of the investigation was to detect differences between the 
phenomena of the different groups of years or of the different classes of days. 
Table XXI. shows the results obtained, including for comparison some already 
published for quiet days. In the case of the diurnal inequality, the first place has 
been given to the sum of the 24 differences from the mean Tor the day. This element 
is much less d jpendent on the accident of local time than is the range, and is probably 
a more accurafe measure of the activity of the forces to which the diurnal inequality 
is due. 
Contrasting ordinary and quiet days, we see that whilst M is invariably greater 
for the former, this is not the case with Pj. Thus Ifi/M—or the fraction of the 
