RANGE AND THE PERIOD OF SOLAR SPOT FREQUENCY. 
547 
A very slight examination of the numbers contained in the foregoing table is 
sufficient to show the existence of distinct epochs of minimum and maximum, the 
successive epochs of minimum and the successive epochs of maximum being separated 
by an interval of ten or eleven years, that between minimum and maximum being about 
four years, and that between maximum and minimum about seven years. 
The numbers of the last table were now employed to form the two curves of 
magnetic diurnal range given on Plate 22. 
The numbers for horizontal force indicate variation of northerly force, and are 
expressed in parts of the whole horizontal force : those for declination imply westerly 
force equivalent in terms of horizontal force to “ horizontal force X sine of number for 
declination.” Or the sine of the number for declination represents the westerly force 
in terms of the horizontal force. The scales for declination and horizontal force on 
Plate 22 are therefore so arranged that each minute of arc of declination is repre¬ 
sented by ’0003 of horizontal force, and so on in proportion. By imagining the scales 
to be extended downwards to their zeros, which will be found to coincide, the com¬ 
parative magnitudes of the diurnal ranges, as well as their variations of magnitude, 
are more clearly perceived. 
One other matter, of no particular significance, may perhaps be mentioned, which is 
that no account is taken of the slow change in the absolute magnitude of the hori¬ 
zontal force : the effect of neglecting it is simply that the two magnetic curves are, 
in the later years, slightly depressed, as compared with the earlier years, but without 
affecting the relation of the curves, each one to the other. 
The upper curve on Plate 22, indicating sun-spot frequency, is formed by laying- 
down corresponding numbers taken from the table given by Dr. Rudolf Wolf in 
his ‘ Astronomisclie Mittheilungen,’ No. 42. They are identical with those contained 
in the table included in Dr. Wolf’s “Memoire sur la Periode commune a la Frequence 
des Taches Solaires et a la Variation de la Declinaison Magnetique ” (‘Memoirs of the 
Royal Astronomical Society,’ vol. xliii., page 199). Dr. Wolf’s monthly numbers of 
relative sun-spot frequency, as determined directly from observation, are given for the 
years under consideration in other parts of the ‘ Astronomische Mittheilungen.’ But 
for the purpose of smoothing their accidental irregularities he treats them (so forming 
the numbers above indicated) precisely as the numbers in our Table I. have been 
treated, in order to eliminate annual inequality. The magnetic curves and the sun¬ 
spot curve are thus strictly comparable. Dr. Wolf’s smoothed table terminates with 
the month of June 1876. The monthly numbers for the succeeding year, to June 
1877, are taken from the ‘Astronomische Mittheilungen,’ No. 46. In laying down the 
sun-spot numbers on Plate 22, one minute of arc of decimation is taken as corresponding 
to 20'0 in sun-spot number. 
An examination of Plate 22 shows immediately the remarkable correspondence 
between the three curves. It will be noticed that the magnetic curves, in the earlier 
years, show more sinuosities than in the later years. Now, until the year 1863 the 
