ON “QUIET” DAYS DURING THE ELEVEN YEARS 1890 TO 1900, ETC. 
399 
especially at Greenwich. When expressed in a Fourier series the annual variation 
shown in Table XXXII. takes the form 
3"-91 + 0"-377 sin(^ + 88°) + 0"-496 sin {21 + 292°), 
where t is measured from the beginning of January exactly as in Table XXX. The 
semi-annual term is here the larger of the two. Its phase angle ditfers by only 1° 
from that obtained in Table XXX. for the corresponding term in the case of the sum 
of the 24 hourly differences in D. It indicates March 20 as the approximate time foi' 
the first maximum. 
The annual term has its first maximum about January 2, and its minimum of course 
six months later; it is thus nearly opposite in phase to the annual term in the 
expressions for the range in the sum of the 24 hourly difiereuces in D. 
Suii-Siwt Relations. Introduction. 
§ 41. General mention lias already been made in § 2, and incidently in other parts 
of the paper, of relations between magnetic phenomena and sun-spot frequency, and 
the numerical results obtained by Wolf and Wolfer for sun-spot frecpiency have 
been already recorded in Table I. There are other metliods of estimating solar 
disturbance, and it would lie of interest to consider likewise data based on these, and 
to investigate the question as to apparent variations in magnetic phenomena with 
variation in the position of the spotted areas in the sun’s surface. I have thought it 
better, however, to confine myself wholly on the present occasion to Wolf and 
Wolfer’s numbers, and to cover a limited portion of tlie ground in a comparatively 
thorough way, rather than to wander at large over the whole field. My own opinion 
is that the true inter-relationships of the several phenomena are hardly likely to he 
reached, and they certainly cannot l)e demonstrated, without a really minute and 
careful study of the facts. 
In treating of sun-spot relations, I shall not adhere strictly to the order followed in 
the first part of the paper, hut shall take first the case of the diurnal periodic changes. 
§ 42. It has been established, largely through the work of Balfour Stewart and 
Ellis, that there is a close connection between ejiochs of maximum and minimum in 
sun-spot frequency and in amplitude of diurnal inequality of magnetic elements. In 
investigating this matter, Mr. Ellis eliminated the annual variation in the amplitude 
of magnetic ranges by assigning to any indi\'idual month the mean amplitude 
deduced from twelve consecutive months, of which it was the central month. I have 
pursued a difiereut method. This consists in expressing the range for any given 
month as a percentage of the arithmetic mean of the ranges for this particular month 
of the year throughout the series of years dealt with. This method is obviously less 
satisfactory when applied to a short number of years than when applied to a period 
including many sun-spot cycles, a defect from which Mr. Ellis’ method is largely free. 
