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.

FROM RECORDS OF THE GREENWICH OBSERVATORY, 1871-1895. 135
should act simultaneously all over a circle of latitude, for that would imply considerable
currents across the earth's surface. It is more likely that the principal action takes
place along a geographical meridian; and if that is the case, the horizontal force should
shew stronger evidence of these lunar periodicities than the declination. There is also the
possibility that what is observed in the daily average of declination is only a remnant of a
variation having the lunar day for its period. In that case the periodicity should disappear when the average position of the needle in a lunar day is subjected to calculation.
If this is the correct explanation it should not be difficult to prove it, for it would
require a much greater amplitude within the lunar day to account for the 0'06 amplitude
found in the daily averages. How much greater may be seen from the following consideration. If from a periodic function cos Kt another is formed by taking averages over a
period 27 we obtain
1 ft+,r
cos Kt dt =- sin K-r cos Kt,
2r t-r ICT
that is a reduction in amplitude of - sin K-r. If 2T is one solar day, 27r/K one lunar
fCT
K7- 28-53
day, - = 2953 hence T-r equals 174~ and the amplitude of the curve obtained by taking
averages is only about the 29th part of that of the original curve. The comparison of
averages of successive days will therefore produce an apparent period having the lunar
month as periodic time and, if the period found above is due to this cause, the amplitude
of the original lunar variation should be 1'"74. Such an amplitude ought to be traceable
without much difficulty.
A thorough enquiry into the nature of lunar periodicities of inagnetic records seems
to me to be of special importance, but requires considerable arithmetical labour; for, to be
conclusive it must be complete. I have been assisted in the numerical calculations which
were necessary in the present investigation by Mr J. R. Ashworth, to whom I desire to
tender my thanks. The expense connected with the numerical work was partially covered
by a small contribution from the Government Grant Fund of the Royal Society.