Memoirs presented to the Cambridge philosophical society on the occasion of the jubilee of Sir George Gabriel Stokes, bart., Hon. LL. D., Hon. SC. D., Lucasian professor.

122 MR SCHUSTER, THE PERIODOGRAM OF MAGNETIC DECLINATION
and those just deduced for the shorter interval. The latter being the mean of values
obtained for the 26 and 27 day periods should, strictly speaking, be put down as belonging
to a period of 26'5 days, but for our purpose it is sufficient to neglect the difference of
half-a-day. Considering that the value of S2 for the 25 years interval represents the
mean of only seven values, the approximation of the ratio of the numbers given for
the intervals of 25 years and one year respectively to the theoretical number 25 is very
remarkable.
Incidentally this agreement shews that the secular variation has been eliminated
sufficiently to leave no appreciable effect on the Periodogram. The last column of
Table X. gives the ordinates of the P. G. for a uniform progressive change of 7'2 per
minute. The original uncorrected figures would have given, according to our previous
deductions (Cases 2 and 3), values for the P. G. made up of the sums of Columns VI. and
il. or III. respectively, and the ratios of these sums would have been widely different from
25. Further consideration of the figures shews that, while possibly a small change in
the assumed value of the secular variation would have brought the numbers of Column iv.
into still nearer agreement with the theoretical number, such a change would amount
to less than a percent., and would be quite uncertain.
The surface of the Periodogram having been determined with sufficient accuracy for
periods varying between 5 and 27 days, it seemed desirable to extend the investigation
1 Unit = 0'0001 -12 /
11- /
10-
9-
7 -6 -4 —
3 -12 -0 5 10 15 20 25
Fig. 1.
to shorter and longer periods. The calculation for a period of 2 days gave very little
trouble. If the alternate numbers in each of the rows of Table I. are added together,
and the differences of these sums are taken, we obtain numbers which, after division by