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Abstract An important extension of our ideas regarding periodicity was made in 1927 when Yule pointed out that, instead of regarding a series of annual sunspot numbers as consisting merely of a harmonic series to which a series of random terms were added, we might suppose a certain amount of causal relationship between the successive annual numbers. In that case the system might be regarded as a physical system possessing one or more natural oscillations of its own, all subject to damping; and the effect of annual random disturbances would be to produce a fairly smooth curve with periods varying in amplitude and length, essentially as the sunspot numbers vary. If we call the departures from their mean of our series u1, u2.., Yule showed that the consequence of a single natural period is an equation like ux = kux-1 - ux-2 + vx, where vx represents the “accidental” external “disturbance”; and if there are two natural periods, ux = k1 (ux-1 + ux-3) - k2ux-2 - ux-4 + vx
Gilbert T. Walker (Wed,) studied this question.