On Permanent Periodicity in Sunspots . n harmonics,* which may have to beseparated out. It is more convenient and suggestive to take out from therecord the periodic part already found and analyse the residue. The residuefor the natural graph (fig. 1) is given in fig. 7, and that for the modifiedgraph of equal amplitudes (fig. 2) is given in fig. 8. In these residues, thetwo defaulting cycles are, of course, conspicuous. The residue when thefundamental simple constituent alone of the 11^-year periodic part has beenremoved, is given as a graph in Prof. Schusters memoir (p. 92), and thepeaks that
On Permanent Periodicity in Sunspots . n harmonics,* which may have to beseparated out. It is more convenient and suggestive to take out from therecord the periodic part already found and analyse the residue. The residuefor the natural graph (fig. 1) is given in fig. 7, and that for the modifiedgraph of equal amplitudes (fig. 2) is given in fig. 8. In these residues, thetwo defaulting cycles are, of course, conspicuous. The residue when thefundamental simple constituent alone of the 11^-year periodic part has beenremoved, is given as a graph in Prof. Schusters memoir (p. 92), and thepeaks that it reveals (mainly, however, in its first .half, which contains thetwo abnormal cycles,—they would hardly be noticed in the second half byitself) suggest to him a possible permanent period of 8*36 years. Ourresidue, when the whole of the ll|~year period is removed, has been testedfor this period by the same process as above, dividing up into three results are shown in fig. 10 : that of the third group containing the most. O 50 100 F^gJO, Components for 8*36 year* modern and exact data undulates closely along the zero axis, and thus showsno such period; the first and second groups both show rises from the zero * In the optical analogy of spectroscopic analysis by a grating, this corresponds tothe overlapping of spectra of different orders. On Permanent Periodicity in Sunspots. 503 axis at the beginning and end, and thus have something in common; butwhen the two abnormal cycles are omitted, the first group gives a graphlying close along the axis, as did the third ; the second result, thus remainingunsupported, is from its form most probably accidental. We thus find noindication of a permanent period near 8*36 years. Our conclusion is that a secular unbroken solar periodicity of about11-i years, controlling superficial solar phenomena, is established firmly, if wemay omit from the record of 160 years the two strongly discrepant cyclesfrom to 1798. We have found
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