ON ERRORS OP OBSERVATION. 141 



To one who is looking for sound principles, I observe 

 that he does not want in this matter the exposition of 

 the consequences of any one law of facility of error, 

 but an account of the general character of those laws 

 to which common sense and daily experience assure 

 him that his faculties and means of observation are 

 subject. The facts of which he stands assured are, 

 that the probability of error does not diminish very 

 rapidly at first, but that as the error we consider grows 

 larger, its probability does diminish very rapidly, and 

 becomes insensibly small for errors of a certain magni- 

 tude and upwards. No curve of comparison, drawn in 

 the manner described in p. 132., will be a true repre- 

 sentation of what we know on this subject, unless it 

 have the general form, of which the following varieties 

 are instances. Now though the preceding results are 

 not strictly true for every curve which has such a form, 

 yet there is a class of curves of this form, some variety 

 or other of which will approach tolerably close to any 

 line which can be drawn to resemble one of those in the 



figure. In every one of this standard class of curves, 

 all the preceding relations are strictly true, and there- 

 fore are nearly true for all the curves which resemble 

 any one of the standard class. Thus though the 

 average error may not always be -}4f of the probable 

 error, yet the former is always some fraction of the 

 latter, not differing very greatly from -J-if. There 

 is another reason for the adoption of this law of error 

 as a standard, for which the reader may consult the 

 fourth appendix to this work. 



