September 15, 1911] 



SCIENCE 



333 



formulated a particularly unfortunate hy- 

 pothesis, 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 illus- 

 trated 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 in- 

 terval 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 ex- 

 treme values. Now when Pogson made his 

 observations of E TJrsce Majoris in 1853-60 

 it was time of halt at an extreme: the 

 period remained stationary and the varia- 

 tion 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 ade- 

 quately: 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 Professor 



Schuster himself tinged with heresy. On 

 the very occasion when he did so much for 

 the observer by presenting his beautiful 

 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 Professor Schuster is not 

 the only one that has been recently pro- 

 posed for dealing with large masses of ob- 

 servations. We have also the methods of 

 Professor Karl Pearson. These have been 

 far more widely adopted for use than the 

 periodogram, and they have also been more 

 adversely criticized. As regards criticism, 

 I think it is fair to say that it has chiefly 

 been directed towards the nature of the ma- 

 terial on which Professor Pearson has used 

 his process than on the process itself, and 

 at present we need not be concerned with 

 it. The processes themselves are soimd 

 enough; one of them, for instance, is much 

 the same 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 insist- 

 ence on the application of it, and the ap- 

 plication to all possible cases. Professor 

 Pearson ceases to look for one principal 

 factor only, and examines all possible fac- 

 tors, just as Professor Schuster examines 

 all possible frequencies. Let us recur for a 

 moment to the words of Sir George Darwin 

 previously quoted. 



