32 



SCIENCE 



[Vol. LV, No. 1411 



that its devotees may go too far with it. How 

 often it occurs that the accuracy of a series of 

 measures as indicated by the probable error is 

 illusory In almost every field of exact meas- 

 urement we have the presence of both acci- 

 dental and systematic errors, and he is an 

 optimist indeed who deals with only the former. 

 It is here that the experimenter is at an ad- 

 vantage, as he naturally is constantly seeking 

 to eliminate undesirable factors, and by con- 

 stantly changing conditions may vary or elim- 

 inate what may be called the systematic errors. 



It has been said that a worker in exact sci- 

 ence usually goes through three stages of atti- 

 tude toward his work. He starts out by con- 

 sidering every small or unexpected discrepancy 

 as due to a physical reality; after being de- 

 ceived a sufficient number of times, he has a 

 reaction, and nothing is proved until it is really 

 proved; he then gradually grows back into a 

 state where he is neither too exultant at the 

 first prospect of a discovery, nor too pessi- 

 mistic over the insufficiency of the evidence for 

 a result which he hopes to establish. We may 

 quote from Langley, who in the discussion of 

 small irregularities of his bolometer records of 

 the solar spectrum said, "When we approach 

 the limits of vision or audition, or of percep- 

 tion by any other of the human senses, no 

 matter how these may be fortified by instru- 

 mental aid, we finally perceive, and always 

 must perceive a condition, a condition still 

 beyond, where certitude becomes incertitude, 

 although we may not be able to designate pre- 

 cisely where one ceases and the other begins. 

 This is always the case, it would seem, on the 

 boundaries of our knowledge in every depart- 

 ment, and it is so here." 



In the estimate of the precision of a given 

 result there is not yet adherence to the logical 

 use of the probable error as a measure of 

 precision or accordance; astronomers long ago 

 adopted this usage, but others seem to get along 

 without it. Only recently I heard in a public 

 address the statement that a certain measure 

 could be made "with an error of one part in a 

 thousand." Just what was meant by this 

 would be difficult to determine, especially as 

 the speaker afterwards said that the "range 

 did not exceed one part in a thousand." These 



loose statements did not come from a beginner 

 but from a master in the art of exact measure- 

 ment. Still another example is found in a 

 recent number of a standard journal: "The 

 maximum error is .1 per cent." This is pre- 

 sumably some sort of estimate of the possible 

 systematic error of the result, but one would 

 think that physicists would come to some 

 common ground in describing their errors, so 

 that they could understand each other. One 

 suspects that here we have simply an illustra- 

 tion of the difference between the observer and 

 the experimenter; the former stays with his 

 measures long enough to have a real basis for 

 computing a probable error, the latter has a 

 few measui-es, and even if he used the formula 

 for the probable error he would be doubtful 

 of its value. Experimenters boast when they 

 have achieved "astronomical precision" in the 

 number of significant figures in their results, 

 but they might equally well cultivate some 

 astronomical accuracy of statement when it 

 comes to describing the reliability or accord- 

 ance of their results. 



The term "astronomical" precision brings to 

 mind the prediction of some years ago that 

 most new discoveries in physics would be in 

 the sixth place of decimals. Whatever else 

 may be said concerning the advances in that 

 science, it will not be maintained that so many 

 significant figures have been necessary to estab- 

 lish the important results. Intelligent lay 

 opinion might be somewhat shocked to learn 

 by what methods astronomers are measuring 

 or estimating distances of stars. A mere guess 

 at the mass of a stellar system may give its 

 distance with far greater accuracy than could 

 possibly be secured by the method of exact 

 measurement. The new things in science con- 

 tinue to be not in the last place but often in 

 the first place of decimals. We should be quite 

 happy to have one significant figure correct in 

 a measure of the size of the visible universe. 



There is one particular field in astronomy 

 where the technique of observing as at present 

 practiced is a constant reminder to the ob- 

 server that either he or some one else had 

 better do some experimenting, and that is in 

 astronomical photogi'aphy. Many an observer 

 during the tedious hours of long exposure 



