EXPEDITION TO POINT BAllROW, ALASKA. 481 



number of simultaneous observations made at different stations, as in the case of the present polar 

 researches, require strict intercoruparability of results, a more definite- proceeding appears desirable. 



I had made use of Peirce's criterion for the rejection of doubtful observations,* or, hero more 

 appropriately expressed, for the separation of observations deviating largely in amount by reason 

 of their following different laws from those to which the ordinary observations are subject; and in 

 using the criterion in such a case it was put forward only with a view of securing some definite 

 rule uniformly applicable. 



The criterion was first employed by me in the discussion of Dr. Kane's magnetic observations 

 of 1853, 1854, 1855, at Van Rensselaer Harbor, North Greenland ; t afterwards for Dr. Bache's 

 magnetic observations of 1840 to 1845 at Philadelphia,! and for the United States Coast Survey 

 magnetic series of I860 to 1806 at Key West, Florida. In these applications, where no great pre- 

 cision is required, its method of application may be much simplified. Thus the mean deviation or 

 the mean difference of any hourly value from its hourly normal may be found, without the trouble 



of forming squares, by the simple expression of f = 1.25 ' | , and the limiting value given by the 



criterion will be = K e, the value of H being a tabular value for the case // = 1, is readily had 

 from Chauvenet's Table X. The limit so found will be the widest one that may be employed, but 

 in special applications it may require contraction, for the reason that the number of the largest 

 disturbances is found to be insufficient for their successful discussion. Instead of using Peirce's 

 criterion, we can, however, arrive at an equally satisfactory fixation of a limit by means of the ex- 

 pressions of either the probable or the mean error of an observation. || We may define the widest 

 limit as that deviation or difference from the mean which exceeds 3.5 times the probable variability 



3 5 

 orprobabledeviationof an observation. This limit corresponds to ' , or to 2.36 times the mean 



deviation (as already used in connection with the criterion). Thus 2 times the mean deviation 

 would be a superior limit, whereas Dr. Lloyd (1874) adopts for the discussion of the disturbances 

 a limit of l.V times the average departure of a reading from its normal. By taking this lower limit 

 we necessarily include a number of disturbances of lesser magnitude ; but should the limit be dra \vn 

 still closer there is danger of confusing the results with values following different laws from those 

 which goveru the larger disturbances. It would be most desirable to investigate the disturbances 

 by a series of graduated limits and falling between these extremes. A limit somewhere between 

 2 and 1A times the mean deviation will probably bo found most satisfactory. To find the mean 



V t 



deviation =1.25 ~ say from an hourly series of observations extending over one year, the diur- 



, tl> ^~ L 



nal as well as the annual variations of the disturbances must be taken into account; and it will 

 suffice to deduce 24 numerical values for e, using for the first mouth the hours and 12, for the 

 second mouth the hours 1 and 13, for the third the hours 2 and 14, etc., and finally to take the 

 average (s) from the 24 individual values so obtained. 



Discussing the hourly variations of the declination recorded in the second year at Uglaamie, 

 where the horizontal component II = 1.936 English units (=0.8927 Gaussian units, or 0.08927 dynes) 

 for October, 1882, the value of e equals 18'.4 nearly ; hence limit by Peirce's criterion = 44', and the 

 same limit for 2 times e ; for twice e the limit is 37', and for 1J e it is 28', which limits separate, re- 

 spectively, 1 disturbed observation in 17 observations, 1 in 12, and 1 in 8. General Sabine's limit in 

 the discussion of Captain Maguire's observations of 1852, 1853, and 1854 was 22'.S7, and the number 



* United States Coast Survey Keport for 1854, pp. 131 to 138; Gould's Astrouomical Journal, No. 83, Cambridge, 

 Mass., April 24, 1855. It is now most readily accessible in Chauvenet's Manual of Spherical and Practical Astronomy, 

 Vol. JI (lirst edition, Philadelphia, 1863). 



! Smithsonian Contributions to Knowledge, Vol. X, 1858. 



t United States Coast Survey Report for 1859, Appendix No. 22. 



$ United States Coast Survey Keport for 1874, Appendix No. 9. 



|| Here, of course, the dill'ereuccs of the tabular hourly readings from their respective hourly normals do not, in 

 any sense, represent errors, every one being as correct an any other; they are variations governed by unknown laws, 

 probably of much complexity. The application of the formnhe of the method of least nquaivN to such phenomena 

 is more or lean precarious ; the pure observing error may be regarded as insignificant. 

 H. Ex. 44 61 



