No. 508] SHORTER ARTICLES AND CORRESPONDENCE 239 



(always assuming that the original data are not collected in a 

 deliberately dishonest or biased manner) is its "probable 

 error." Unfortunately this statement of the case appears not 

 to carry conviction to the non-statistical worker. It has seemed 

 to the writer that if the assertion made by the statistician 

 regarding the point under discussion is true, it ought to be pos- 

 sible to demonstrate it in such a manner as to carry conviction 

 to anybody. 



With this object in view the experiment to be described was 

 tried. Some time ago the writer measured for another purpose 

 the lengths of 450 hens' eggs. The measurements were made 

 with a large steel micrometer caliper manufactured by Browne- 

 Sharpe & Co., reading directly to hundredths of a millimeter. 

 The utmost care was exercised in the making of the measure- 

 ments ; they were all made under the same conditions as to light, 

 temperature, etc. ; the caliper was held in a specially constructed 

 stand to get rid of the error arising from expansion and con- 

 traction if it is held in the hand ; the micrometer screwhead was 

 fitted with a ratchet which mechanically insures that the same 

 pressure shall be exerted on the object in every case ; all meas- 

 urements were made by the same observer who has had consider- 

 able experience in close micrometer measuring. The maximum 

 length was the thing measured. There is every reason to believe 

 that these measurements to hundredths of a millimeter are as 

 accurate as it is possible to make them with the instrument used. 

 This being the case all will agree that any statistical constant 

 deduced from them can be held to be accurate to hundredths of 

 a millimeter at least. Now let it be supposed that these eggs 

 had been measured only to the nearest millimeter instead of to 

 the nearest hundredth of a millimeter. By how much would the 

 statistical constants deduced from the "millimeter" data differ 

 from those deduced from the "hundredth millimeter data?" 3 _ 



To answer this question it is necessary to calculate some statis- 

 tical constant for the two sets of data. The mean was chosen 

 as the simplest possible constant. The actual measurements 

 to hundredths of a millimeter were used as one set of data. The 

 ^millimeter" data were obtained by discarding the decimals 

 of the original measurements. In this discarding a record was 

 raised 1 mm. whenever the decimal portion of the original 



3 The biometrician will of course, recognize that the problem here in- 

 volved is the same as that of the influence of the fineness of grouping on 



