448 BENJAMIN PEIRCE. 



Coast Survey, induced Professor Peirce to take up the subject of the 

 longitude determinations in the Survey. As a result, there appeared 

 in the successive volumes of the " Coast Survey Reports," communica- 

 tions from him upon the several questions that arise in the treatment 

 of that subject. The most noteworthy I'eferred to the determination 

 of our longitude from Greenwich, since local differences were deter- 

 mined by the telegraphic method. The whole subject of errors of ob- 

 servations, the law of facility of error which is assumed in the method 

 of least squares, its limits and defects, and the habits of observers, 

 were carefully examined. The method of occultations was decided 

 to admit of greater accuracy than any other that was then available, 

 and the occultations of the Pleiades to furnish the most convenient 

 means of its application. Formulae and tables were prepared, old 

 observations collected, and new ones made to apply this method. The 

 question of our longitude is now, thanks to the ocean telegraph, one 

 of history ; but the questions of errors in observing, which Professor 

 Peirce so thoroughly treated, will always be of practical import. 



It seems as though there was a connection between this engagement 

 with the Coast Survey and the appearance, in July, 1852, in Gould's 

 " Astronomical Journal," of an article by Professor Peirce, entitled, 

 " Criterion for the Rejection of Doubtful Observations." His object 

 was to solve this problem : There being given certain observations, of 

 which the greater part is to be regarded as normal, and subject to the 

 ordinary law of error adopted in the method of least squares, while 

 a smaller unknown jaortion is abnormal, and subject to some obscure 

 source of error, to ascertain the most probable hypothesis as to the 

 partition of the observations into normal and abnormal. This method 

 or rule given for deciding whether an observation had better be left 

 out of account has received the name, " Peirce's Criterion," and must 

 be regarded as one of his best contributions to science. Tables for 

 use in applying it wei"e soon afterwards published by Dr. Gould. 



The "Criterion" has been criticised by Professor (now Sir G. B.) 

 Airy as defective in its foundation and illusory in its results ; and he 

 was even of opinion that no rule for the exclusion of an observation 

 can be obtained by any process founded purely upon a consideration 

 of the discordance of those observations. This position of the Astron- 

 omer Royal must be regarded as entirely untenable ; for no observer 

 hesitates to call a widely discordant observation a mistake, and to reject 

 it (when he can find no other reason for so doing), simply because of 

 that discordance. AVhat the mind thus instinctively does, there must 

 be basis at least for a rule for doing. Professor Airy's objections were 



