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.

116 MR SCHUSTER, THE PERIODOGRAM OF MAGNETIC DECLINATION
Table III. gives the figures so corrected, and these were plotted down on a suitable
scale, and curves drawn, joining the ordinates by straight lines. The Fourier coefficients
were obtained by means of Coradi's Harmonic Analyser, belonging to the City Guilds
of London Institute, which Prof. 0. Henrici kindly placed at the disposal of his assistant
Mr H. Klugh for the purpose.
Table IV. gives the values of the coefficients of the series
a1 cos Kt + a2 cos 2ct +......
+ bi sin Kt + b2 sin 2ct +......
TABLE IV,
Days in No. of
Period ai b1 a, b, a( b3 a4 b4 b5 Periods
24 + 752 +8-92 +6-48 + 008 - 232 - 448 - 332 + 544 + 124 + 308 380
25 -080 - 096 + +444 - -276 - 304 -4-00 + 368 + 648 + 404 +1-76 365
26 -0-68 -13-08 - 6-60 -- 316 + 3-92 + 0-24 - 3-44 -2-16 - 3-36 + 1-92 351
27 + 044 -11-20 +8-76 - 288 + 344 + 628 - 308 - 372 - 116 + 1-16 338
28 + 004 + 8-36 - 596 + 2-56 + 2-16 + 1-96 - 1-52 - 528 - 308 - 020 326
29 + 4-68 - 052 - 456 + 296 - 128 - 3-40 - 056 + 188 + 396 + 108 314
30 -13-64 - 800 - 2-36 + 4-64 + 2-16 - 4-12 - 020 + 0-80 - 0-96 + 3-52 304
To obtain comparable figures a further reduction is necessary. The number of rows
included in Table III. and indicated in the last column of Table IV. differs according
to the period, being larger for the shorter periods. If Fourier's analysis had been
applied to the original series of numbers made up of the actual observed values of
declination, the factors obtained would have been smaller than those given in Table III. in
proportion of the number of periods included. It is not necessary to perform the
division for each coefficient separately, as the ordinates of the Periodograph depend only
on the square of the amplitude, viz. r2 =a,2+b,2; r22=a22 + b22; etc. Table V. gives the
reduced squares R12, R22, which correspond to R2 in (2), r being the Ist of January,
1869, T the number given in the first column of Table V., and n the number given
in the last column of Table III.
It is seen that the values of R2 are subject to considerable variations, R12 being
for instance more than 100 times larger for the 26 day period than for the 25 day
period. According to the reasoning uniformly employed by previous investigators, this
would prove a real existence of the 26 day period, but the theory of probability shews