314 TRANSACTIONS OF SECTION A. 



advance in knowledge resulting, not from observations made with regard to any 

 particular theory, but from the simple collection of facts and the arrangement of 

 them in all possible ways, the very method which has been despised and condemned. 

 Let us contrast with this the method hitherto adopted, which has been to hunt 

 for some particular possible cause which will give the eleven-year period. Thus 

 Professor E. W. Brown suggested 3 in 1900 that the eleven-year cycle was due to 

 the tidal action of Jupiter, altered periodically by two causes :— 



By Jupiter's eccentricity 

 By the motion of Saturn 



and he supports his contention by an ingenious and striking diagram, which 

 seems to explain not only the main cycle, but its anomalies. (This Paper is in 

 fact the exception above referred to.) But if his contention is correct the 

 periodogram should show bright lines at 1186 and 9'93 years, which it does not. 

 This is worth noting, since it is sometimes said that there is nothing new in 

 Professor Schuster's method, which is true enough in one sense, since it is simply 

 the analysis of Fourier. The novelty consists, firstly, in calling attention to the 

 necessity of applying the analysis in all cases, a necessity which I venture to 

 think was overlooked in this instance by so able a mathematician as Professor 

 Brown; and, secondly, in the insistence on the examination of all periods, irrespec- 

 tive of any particular theory or preconception. And in this second character the 

 method seems to me to cut at the root of the canons of procedure which have 

 found favour hitherto. 



As a second instance I present with much more diffidence a few results which 

 seem to emerge from a very laborious analysis of the rainfall at three or four 

 stations, for which Professor Schuster and myself are jointly responsible. There 

 is some evidence for a cycle of 600 days in the Greenwich rainfall to which a 

 further cycle in the quarter period (150 days) lends support. On analysing the 

 Padua records it is found that these cycles do not exist, but it seems quite pos- 

 sible that there are cycles of rather shorter period, viz., 594 days and 148^ days : 

 the relation of four to one being maintained. The separate links in this chain are 

 none of them very strong, but they seem to hang together, and there is certainly 

 a case for further investigation. But would this case have been likely to present 

 itself in any other way than by the examination of the whole periodogram ? I find 

 it very difficult to think, even now the periods are suggested, of any theoretical 

 cause : to let the facts speak for themselves took much time and labour, but I 

 venture to think that we might have waited far longer, and cudgelled our brains 

 much more, before we got the clue by formulating hypotheses of causation. 



A new method is not adopted widely all at once. Professor Whittaker has, 

 T am glad to say, begun to apply the method to variable star observations, and is 

 already hopeful of having obtained valuable information in the case of the star 

 SS Cyqni. Possibly we may hear something from him at this meeting. Mean- 

 while I take the opportunity to remark that the history of variable star observa- 

 tion affords us many lessons as to the desirability of simply accumulating obser- 

 vations and letting them speak for themselves instead of being guided by a 

 theory on hypothesis. Let me give an instance. One of the fathers of variable 

 star-observing, the late N. R. Pogson, made a series of excellent observations of 

 the star I?. Ursce Majoris in the years 1853 to 1860. He then seems to have 

 formulated a particularly unfortunate hypothesis, viz., that he knew all abcut 

 the variation ; and he accordingly only made sporadic observations in succeeding 

 years. Now this star, along with many others, varies in a manner which may be 

 illustrated from the occurrence of sunrise. The average interval between two 

 sunrises is exactly twenty-four hours : but this is only the average. In March 

 the sun is rising two minutes earlier every day, and the interval is therefore 

 two minutes short of twenty-four hours ; as the year advances the daily gain 

 slackens, and at mid-summer the interval is exactly twenty-four hours : then the 

 sun begins to rise later each day, and the interval exceeds twenty-four hours and 

 so on : so that there is a regular yearly swing backwards and forwards through 

 a mean value : and as in the case of all such swings there is a sensible halt at 

 the extreme values. Now when Pogson made his observations of 7?. Ursa Majoris 



2 Monthly Notices fi.A.S., lx., p. 600. 



