294 



NATURE 



[August 31, 191 1 



of variable star-observing, the late N. R. Pogson, made 

 a series of excellent observations of the star R Ursaj 

 Majoris in the years 1853 to 1S60. He then seems to have 

 formulated a particularly unfortunate hypothesis, viz. that 

 he knew all about 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 midsummer 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 Pog- 

 son made his observations of R Ursa; Majoris in 1853-60 

 it was time of halt at an extreme ; the period remained 

 stationary, and the variation repeated itself eleven times 

 in closely similar fashion, so that Pogson concluded it 

 would continue in the same way. How many instances 

 suffice for an induction?. Many inductions have been based 

 on fewer than eleven. Unfortunately, the period was just 

 beginning to change sensibly, and we lost much valuable 

 information, for no one else repaired Pogson 's neglect 

 adequately ; and the whole swing of period occupies about 

 forty years, so that the opportunity of studying the changes 

 he missed has only quite recently returned. We are thus 

 reminded how disastrous may be a break in the record. 

 It should be one of the articles of faith with an observer 

 that the record is sacred, and must not be broken. Most 

 of them, indeed, act on that principle already ; but there 

 are heretics, and it pained us to find even Prof. Schuster 

 himself tinged with heresy. On the very occasion when 

 he did so much for the observer by presenting his beau- 

 tiful method, he suggested that it might even be advisable 

 to drop observing for a time in order to apply the method 

 to accumulated observations. He may possibly be right, 

 but the observer had better believe him wrong. There 

 ought to be an " observer's promise," like the promise of 

 the boy scout ; and one part of it should be not to inter- 

 rupt the record, and another should be to publish the 

 observations regularly, and never to let them accumulate 

 beyond five years. 



The method of Prof. Schuster is not the only one that 

 has been recently proposed for dealing with large masses 

 of observations. We have also the methods of Prof. Karl 

 Pearson. These have been far more widely adopted for 

 use than the periodogram, and they have also been more 

 adversely criticised. As regards criticism, I think it is 

 fair to say that it has chiefly been directed towards the 

 nature of the material on which Prof. Pearson has used 

 his process than on the process itself, and at present we 

 need not be concerned with it. The processes themselves 

 are sound enough ; one of them, for instance, is much the 

 came as the old method of least squares in a simple form. 

 But if the same criticism is made as has been made on 

 the method of the periodogram, viz. that it is not new, 

 we can reply in almost the same words in the two cases : 

 the mathematical calculus may not be new ; the novelty is 

 the insistence on the application of it, and the applica- 

 tion to all possible cases. Prof. Pearson ceases to look 

 for one principal factor only, and examines all possible 

 factors, just as Prof. Schuster examines all possible 

 frequencies. Let us recur for a moment to the words of 

 Sir George Darwin previously quoted. 



" A mere catalogue of facts, however well arranged, has 

 never led to any important scientific generalisation. For 

 in any subject the facts are so numerous and many-sided 

 that they only lead us to a conclusion when they are 

 marshalled by the light of some leading idea." 



Let us take, for instance, a catalogue of variable stars 

 such as those of Mr. Chandler. Particulars for each star 

 are given in separate columns, exclusive of the name and 

 number. We might wait long for a leading idea to guide 

 us in marshalling the facts, and, so far as I know, we 

 have waited till now without any such idea occurring to 

 anyone. But Prof. Pearson insists on the plain duty of 



determining the correlation between each and every pair 

 of these columns, and any others we may be able to add. 

 Anybody could have made the suggestion, and there was 

 plenty of elementary mathematical machinery in existence 

 for carrying it out ; but, so far as I know, nobody did, 

 any more than the critics of Columbus suggested how to 

 stand up an egg. But the suggestion having been made 

 by Prof. Pearson, it was so clearly sound that I did what 

 lay in my power to follow it up, with the result that 

 certain correlations were at once indicated which at least 

 pave the way for further inquiry. If we cannot say more 

 than this, it is simply because the catalogue of facts was 

 not large enough. So far from the observers having 

 wasted their energies by observing without any theory to 

 guide them, more work of the same kind would have 

 been welcome, for it would have reduced the probable 

 error of the correlations indicated. As an example, I may 

 quote the following. It has already been mentioned that 

 a variable star maximum, though it may recur after a 

 more or less definite period, on the average, is subject to 

 a swing to and fro like the time of sunrise. Let us call 

 the average interval the day of the star and the period of 

 swing the year, without implying anything more by these 

 names than appears in the analogy. Then I found ' that 

 the day and the year were correlated, the value of the 

 coefficient being 



r = 0-56 + 008. 

 Having obtained this clue, it was interesting to use it for 

 the elucidation of individual problems. The days of many 

 stars are by this time pretty well known, but their years 

 are very uncertain. In nine or ten cases the assessment 

 of the vaguely known year was under revision, and in all, 

 without exception, the revised assessment tended in the 

 direction of the formula. In one case (S Serpentis) the 

 formula suggested the solution of a long-standing puzzle. 3 

 Finally, the inquiry is suggested whether our own sun 

 may be treated as a variable star with a period or day 

 of eleven years, in which case its time of swing a year 

 should be about seventy-five years if the formula is strictly 

 linear. There are found to be indications of a swing of 

 this order of magnitude, though the time given by the 

 periodogram method is fifty-four years. 3 If the relation 

 between year and day is not strictly linear, these figures 

 could easily be reconciled for a case lying so far outside 

 the limits within which the formula was deduced. But 

 the ultimate successful establishment of the connection is 

 of less importance for our present purpose than to notice 

 the fruitfulness of the method of suggestion, which is as 

 mechanical as Bacon himself could have wished. 



Let us admit frankly that there is an appearance of 

 brutality about such methods. Is our method of search 

 to be merely the old and prosaic one of leaving no stone 

 unturned? We have been led to believe that there should 

 be more of inspiration in it : that a true man of science 

 should have some of the qualities of that fascinating hero 

 of fiction, Mr. Sherlock Holmes, who picks up his clue 

 and follows i! unerringly to the triumphant conclusion. 

 Such qualities will do the man of science no possible 

 harm : indeed, they will be of the utmost value to him. 

 The point to which I am now calling attention is the 

 change in nature of the opportunities for using them, 

 which are becoming every day more confused. Sir Conan 

 Doyle, in the exercise of his art. keeps our attention fixed 

 on a single trail : he conceals from us by mere omission 

 the numerous trails which cross it. We admire the skill 

 of the Indian who pursues an enemy through the track- 

 less forest ; but his success depends on the simplicity 

 hrought by this very tracklessness, and would be imperilled 

 if there were numerous tracks. It may be remarked, 

 however, that there is a still higher sagacity — that of the 

 hound who. even among a number of tracks, can pick out 

 the right one by scent. Let us imagine for a moment 

 that the scientific man can be endowed in the futun 

 training or by some new invention, with a faculty of this 

 kind, so that he may unerringly pursue a single trail even 

 when it is crossed and recrossed by others. Then, in the 

 terms of this metaphor, I draw attention to the fact that 

 he has still to determine which is the right trail, and that 

 in general he can only do so by pursuing each in turn to 

 1 Monthly Notices R.A.S.. lxviii., p. 544. ^ Tbid., p. 156- " /.''•''</., P- «S9 



NO. 2183, VOL. 87] 



