Meantime M. Rudolf Wolf, transferred to the direction of the Zürich Observatory, where he died, December 6, 1893, had relaxed none of his zeal in the investigation of sun-spot periodicity. A laborious revision of the entire subject with the aid of fresh materials led him, in 1859,[486] to the conclusion that while the _mean_ period differed little from that arrived at in 1852 of 11.11 years, very considerable fluctuations on either side of that mean were rather the rule than the exception. Indeed, the phrase "sun-spot period" must be understood as fitting very loosely the great fact it is taken to represent; so loosely, that the interval between two maxima may rise to sixteen and a half or sink below seven and a half years.[487] In 1861[488] Wolf showed, and the remark was fully confirmed at Kew, that the shortest periods brought the most acute crises, and _vice versâ_; as if for each wave of disturbance a strictly equal amount of energy were available, which might spend itself lavishly and rapidly, or slowly and parsimoniously, but could in no case be exceeded. The further inclusion of recurring solar commotions within a cycle of fifty-five and a half years was simultaneously pointed out; and Hermann Fritz showed soon afterwards that the aurora borealis is subject to an identical double periodicity.[489] The same inquirer has more recently detected both for auroræ and sun-spots a "secular period" of 222 years,[490] and the Kew observations indicate for the latter, oscillations accomplished within twenty-six and twenty-four days,[491] depending, most likely, upon the rotation of the sun. This is certainly reflected in magnetic, and perhaps in auroral periodicity. The more closely, in fact, spot-fluctuations are looked into, the more complex they prove. Maxima of one order are superposed upon, or in part neutralised by, maxima of another order;[492] originating causes are masked by modifying causes; the larger waves of the commotion are indented with minor undulations, and these again crisped with tiny ripples, while the whole rises and falls with the swell of the great secular wave, scarcely perceptible in its progress because so vast in scale.