312 TRANSACTIONS OF SECTION A. 



played. This being so, it is only necessary to repeat the process for notes of 

 different pitch. But though this can be stated so simply, the carrying out in 

 practice may involve immense labour, by reason of the number of separate notes 

 to be investigated. It is not merely that these will extend from low growls by 

 the double bass to high squeaks by the fiddles, but that their variety within 

 these wide limits will be so great. The series is really infinite. We might in- 

 deed prescribe a certain scale of finite intervals for the main notes, as in a piano : 

 but the harmonics of the main tones would refuse to obey this artificial arrange- 

 ment and would form intermediate pitches which must be properly investigated 

 if our analysis is to be complete. Moreover the orchestral instruments will not 

 keep to any such prescribed intervals, but will insist on departing from them 

 more or less, according to the skill of the performer. There is a story told of an 

 accompanist who vainly tried to adjust the key of his accompaniment to the erratic 

 voice of a singer. At length in exasperation he addressed him as follows : 

 ' Sir, I have tried you on the white notes, and I have tried you on the black 

 notes, and I have tried you on white and black mixed : you are singing on the 

 cracks ! ' Some instruments will almost certainly ' sing on the cracks ' so that 

 we shall not easily escape from the examination of a very large number of pos- 

 sibilities indeed — we may well call them all the possibilities within the limits 

 of audibility. The illustration is already sufficiently developed for provisional 

 usp. My suggestion is that science has only dealt so far with the easy records 

 and that the genuine hard work is to come. If we can imagine a number of deaf 

 persons turned loose among a miscellaneous collection of gramophone records, 

 with instructions to make what they could of them, we can readily imagine 

 that they would pick out those of single instruments first. We must make the 

 researchers deaf so that they may not use the beautiful mechanism of the human 

 ear which has as yet no analogue in scientific work. Possibly something corre- 

 sponding t-o this wonderful and still mysterious mechanism may ultimately be 

 devised, and then the course of scientific research may be fundamentally 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 hypothetical case be a sensational event, reflecting 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 Schuster'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 meteorological element such as tem- 

 perature or rainfall. When these records are put in the form of a diagram in 

 the familiar way we get a wavy line, which has much in common with that 

 traced by a gramophone needle on a smaller scale. The sight of the complexi- 

 ties is almost paralysing, especially when those who would otherwise attack the 

 problem are deterred by the emphatic assertion that it is useless to do so with- 

 out the equipment of some guiding hypothesis. Most of the obvious hypotheses 

 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 labour 

 is great, but the genuine observer is not afraid of labour : 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 practice the work always resolves itself into a 

 series of finite steps, owing to the finite extent of the observations. 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 frequency 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 available period of observation. Indeed 



