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. 113
within that year, but some of which may have belonged to December of the preceding
or January of the following year.
Table I. gives the figures for the 24 day period, the last three columns indicating
the date of the first and the last observation made use of in the corresponding row
and the number of rows included in the year, 356' 70 Ineaning the 356th day of 1870.
The unit in the first three Tables is 0'1 of a minute of arc; in the remaining Tables,
unless otherwise stated, it is the minute of arc.
The columns of Table I. and of the corresponding ones for other periods were added
up, and the results, after subtracting a constant for each row, are given in Table II.
Table II. clearly shews the effects of secular variation, and we must consider in
how far it is necessary to take any notice of this variation. If our observations extended
over an indefinite time, Fourier's analysis would itself perform all that is required, and
each period would be totally independent of all others. But our investigations have
been limited to a range of time of 25 years, and the secular variation involves a period
much longer than this. The progressive change of declination will add terms to the
periodic series which it is easy to evaluate with sufficient accuracy. If we take the
change to be uniform and equal to -ct, Fourier's theorem applied to the interval 0 to
T gives us
cT cT (. 27rt 1. 47rt 1. 67r )
- ct= - s-+- T sin sin T+ +n +...............(3)
The effect of such a uniform progressive change would be to leave the cosine
cT
terms unaffected, and to add T to all sine terms of period T.
7r
As it is our object to separate all real from accidental periodicities, we are justified
in eliminating all known effects either totally or partially according to convenience.
The average magnetic declination at Greenwich during the year 1893 was 2052.7
less than during 1869, giving during 25 years a change of almost exactly 3~. Throughout
this investigation the magnetic declination has therefore been assumed to be made up
of a uniform progressive diminution of 7'2 per year added on to more or less irregular
changes, the latter only being subjected to Fourier's analysis. No assumption is made
as to the secular variation being either uniform in character or having exactly the
above magnitude. We have eliminated from our results a large portion of the secular
variation, but it is immaterial whether it is entirely eliminated or not. Should it be found
desirable to return to the uncorrected figures and to calculate the Fourier coefficients,
including the effects of secular variation, it will be easy to do so with the help of
equation (3). As the unit in Table II. is 01 of a minute, the correction is made
by adding to successive columns, successive multiples of 1800/n, where n is the number
of days in the period. For example, in the 24 day period, 75 is added to the second
number, 150 to the third, and so on.
VOL. XVIII. 15