with Remarks on the Law of Frequency of Error. 37 



roughly at first, but proceeding with more care as the residuum 

 diminishes and the differences become less obvious. The last 

 remaining object will be p. Similarly we find q. Then m will 

 be found in the same way from the group compounded of those 

 that were sorted to the right from P and to the left from Q. 



There are not a few cases where both the ordinary method 

 and that by intercomparison are equally applicable, but in 

 which the latter would prove the more rapid and convenient. 

 I would mention one of some importance to those anthropologists 

 who may hereafter collect data in uncivilized countries. A bar- 

 barian chief might often be induced to marshal his men in the 

 order of their heights, or in that of the popular estimate of their 

 skill in any capacity ; but it would require some apparatus and 

 a great deal of time to measure each man separately, even sup- 

 posing it possible to overcome the usually strong repugnance of 

 uncivilized people to any such proceeding. 



The practice of sorting objects into classes may be said to be 

 coextensive with commerce, the industries, and the arts. It is 

 adopted in the numerous examinations, whether pass or compe- 

 titive, some or other of which all youths have now to undergo. 

 It is adopted with every thing that has a money-value; and all 

 acts of morality and of intellectual effort have to submit to a 

 verdict of " good," " indifferent," or " bad." 



The specimen values obtained by the process I have described 

 are capable of being reproduced so long as the statistical condi- 

 tions remain unchanged. They are also capable of being de- 

 scribed in various ways, and therefore of forming permanent 

 standards of reference. Their importance then becomes of the 

 same kind as that which the melting-points of well-defined alloys 

 or those of iron and of other metals had to chemists when no re- 

 liable thermometer existed for high temperatures. These were 

 excellent for reference, though their relations inter se were sub- 

 ject to doubt. But we need never remain wholly in the dark as 

 to the relative value of our specimens, methods appropriate to each 

 case being sure to exist by which we may gain enlightenment. 

 The measurement of work done by any faculty when trained and 

 exerted to its uttermost, would be frequently available as a test 

 of its absolute efficacy. 



There is another method, which I have already advocated and 

 adopted, for gaining an insight into the absolute efficacies of 

 qualities, on which there remains more to say. Whenever we 

 have grounds for believing the law of frequency of error to apply, 

 we may vjork backwards, and, from the relative frequency of 

 occurrence of various magnitudes, derive a knowledge of the true 

 relative values of those magnitudes, expressed in units of pro- 

 bable error. The law of frequency of error says that (t mag- 



