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.

134 MR SCHUSTER, THE PERIODOGRAM OF MAGNETIO DECLINATION
search of periodicities has been that of Prof. v. Bezold whose work had reference to
the frequency of thunder-storms. He gives 25'84 days as the length of his period, but
it was really only the semi-period which shewed a large amplitude. The numbers 25 84
and 2a5825 lie so near together that it will be wise to keep an open mind as to the
possibility of some real periodic time of that length. But it must be understood that
the record of Greenwich declination extending over 25 years shews nothing beyond a
slight indication of such a period. An intensity of '006 corresponds to an amplitude
of '077 minute of arc, and it can be definitely asserted as the result of this enquiry
that there is no period between 25'5 and 27'5 days which had a larger amplitude at
Greenwich during the years 1871-1895.
VII. LUNAR PERIODICITIES.
One of the principal objects of this investigation was to prove or disprove the
suspected lunar period in the daily average of magnetic declination. The clustering of
phases round the line BB', Plate IV., shews that observation gives a somewhat larger
amplitude than the average for a period of 27'327 days which lies very near the length
of the tropical month. The two periods, that of tropic revolution and that of synodic
revolution, were therefore specially treated, the result being exhibited in Table XV. It
TABLE XV.. Square of Square of
Period Amplitude K Semi-period Amplitude K
27-32 -002352 2-24 13-66 -000819 2-16
29-53 -000026 -25 14-77 -002876 7-56
is seen at once that there is a strong indication of a period having as its time half
the period of the synodic month. The value of Ic which is 7-56 is considerably higher
than any other given within the whole range of investigated periods. An accidental
coincidence is not excluded, for as calculation shews it may happen once in every 2000
trials that such a large value should be found for K. We can only assert therefore
that there is a probability of 2000 to 1 that the moon has a true effect on magnetic
declination. The amplitude is only '054 minute of arc and the strong evidence afforded
of the real existence of a periodicity having such a small amplitude shews, I think,
the value of the method which has been adopted in this investigation. As regards the
phase of action no certain conclusions can at present be drawn; the maximum westerly
declination occurred on the average during the years under examination between 2 and
3 days after new and full moon. Nothing is of course asserted as to the reason why
the moon should affect the declination needle, but the action is probably a very indirect
one. It would be important to extend the investigation to the other components of
magnetic force and to other localities. It is highly improbable that a westerly force