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SCIENCE 



[N. S. Vol. XXXIV. No. 872 



yet no analo^e in scientific work. Pos- 

 sibly something corresponding to this won- 

 derful and still mysterious mechanism may 

 ultimately be devised, and then the course 

 of scientific research may be fundamen- 

 tally altered : but for the present we must 

 regard ourselves as deaf, and as condemned 

 to work by patient analysis of the records. 

 It is perfectly natural, and even desirable, 

 to begin with the easy ones, and the finding 

 of an easy one would no doubt in our hy- 

 pothetical case be a sensational event, re- 

 flecting credit on the lucky discoverer, who 

 would be hailed as having detected a new 

 law, i. e., a new simple case. But sooner 

 or later these will be used up and we must 

 attack the more complex orchestral records 

 in earnest. Shall we find that the best 

 music is still to come, as our illustration 

 suggests ? 



But we must return to Professor Schus- 

 ter's suggested plan of work. It is closely 

 similar to that already sketched for dealing 

 with a complex gramophone record. Let 

 us consider the record of any meteorolog- 

 ical element such as temperature or rain- 

 fall. When these records are put in the 

 form of a diagram in the familiar way we 

 get a wavy line, which has much in com- 

 mon with that traced by a gramophone 

 needle on a smaller scale. The sight of the 

 complexities is almost paralyzing, espe- 

 cially when those who would otherwise at- 

 tack the problem are deterred by the em- 

 phatic assertion that it is useless to do so 

 without the equipment of some guiding 

 hypothesis. Most of the obvious hypoth- 

 eses have of course already been tried, and 

 the majority of them have failed. It is to 

 Professor Schuster that we owe the vitally 

 important advice to disregard hypotheses 

 and make a complete analysis of the record. 

 Of course the labor is great, but the genuine 

 observer is not afraid of labor: he has a 

 right to ask, of course, that it shall not be 



interminable: and when we are told that 

 we must examine an almost infinite series 

 of possibilities there would seem to be some 

 danger of this. But in practise the work 

 always resolves itself into a series of finite 

 steps, owing to the finite extent of the ob- 

 servations. A definite illustration will 

 make this clear. Suppose we have ninety 

 years of rainfall and we test the record for 

 a frequency of nine years, which would 

 run through its period ten times: we must 

 certainly test independently for a fre- 

 quency of ten years, which would only run 

 through its period nine times, and thus lose 

 one whole period on the former wave : and 

 so also for a possible frequency of nine 

 years and a half, and of nine years and a 

 quarter. But a frequency of nine years 

 and one day would not be distinguishable 

 from that of nine years, for the phase 

 would only change 1° in the whole avail- 

 able period of observation. Indeed the 

 same might be said of aU frequencies be- 

 tween nine years and nine years and one 

 month : for the extreme difference of phase 

 would not exceed 40°. But in course of 

 time when the series of ninety years' ob- 

 servations become 900 years, the differences 

 of phase will approach or exceed a com- 

 plete cycle, and we must accordingly nar- 

 row the intervals between frequencies 

 chosen for examination. 



The length of the series of observations 

 is thus an important factor in our proce- 

 dure, for which Professor Schuster has in- 

 dicated a beautiful analogy. Our illustra- 

 tions hitherto have been provided by the 

 science of sound, but we may also gather 

 them from that of optics. Testing a series 

 of rainfall observations for a periodicity is 

 like examining a source of light for a defi- 

 nite bright line. The process of computa- 

 tion indicated by Fourier gives us what 

 corresponds to the measured brilliance of 

 the bright line; and the complete process 



