350 PROCEEDINGS OF THE AMERICAN ACADEMY 



NovEMBEn 22, 1877. 



Respecting Prof. Peirce's Criterion, I venture a few remarks : — 



Laro-e errors may arise either from an accumulation of a number of 

 small ones, having their origin in different sources, as is recognized in 

 the theory of combination of errors, and as such they may be regarded 

 as normal (even if quite large), provided they belong to a series of an 

 indefinitely large number of observations. Practically, we have but a 

 few observations (most frequently less than one hundred), and while 

 certain sources of error may combine to the production of large ones, 

 their actual appearance in a short series of observations must injuriously 

 affect the most probable result (say the mean) deducible from the 

 series. Here we need the means of separation, and the Criterion logi- 

 cally performs this. 



Or large errors may arise from bad observations (due to inatten- 

 tion of observer, witliout being aware of it), from the presence in 

 this particular case of an unsuspected constant error, or even from an 

 accidental slip (necessarily not altogether outside the possibility of its 

 being due to other causes admissible) : all such large errors having no 

 recognized place in the adopted law of the occurrence of error must be 

 subject to rejection, for which we need the Criterion. 



Supposing the probable error of a result before rejection = s and 

 after rejection = £j, the latter value has some times been adopted, 

 which I think is generally not admissible, the value e would better be 

 retained as evidence that rejections have been made. If fj is retained, 

 we may fall into the error, of again trying on the Criterion * based 

 upon «!. 



Having used the Criterion for the last twenty years in various 

 investigations, I found it uniformly gave excellent discrimination, and 

 do not remember a single case where it came in conflict with proper 

 judgment based upon experience. Of course in those instances where 

 we have antecedently a knowledge of s, we would employ this value 

 in preference to a value deduced from a single series of observations : 

 in such cases, observations are frequently retained by the Criterion 

 which otherwise would have been rejected. If it errs at all, it may 

 sometimes appear to cut too deep ; but our general experience is that 



* I remember a rather curious case of this kind, where an observer rejected 

 successively three times, each time deducing and starting from a new probable 

 error, when he became alarmed for the safety of the rest of his observations 

 and stopped further testing them. 



