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 u 1, u 2.., Yule showed that the consequence of a single natural period is an equation like ux = ku x -1 - u x -2 + vx , where vx represents the “accidental” external “disturbance”; and if there are two natural periods, ux = k 1 ( u x -1 + u x -3) - k 2 u x -2 - u x -4 + vx
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