66 Mr. J. D. Hamilton Dickson. [Jan. 21, 



Q in all positions is Z>, and that of Q relatively to M is c. The ordi- 

 nary law of error is to be assumed. 



If in any one observation, MQ=#, Qq=y, then the law of error 

 requires 



/»2 ,,,2 



- + l (12) 



c 2 Z> 2 K ' 



to be a minimum, subject to the condition 



x-\-y=a, a constant. 

 Hence we have at once, to determine the most probable values of 



x y a /io\ 



and the most probable position of Q, measured from M, when g's ob- 

 served distance from M is a, is 



It also follows at once that the probable error v of Q (which may 

 be obtained by substituting a— x for y in (12) ) is given by 



11,1 he 



jt^+f mv (14) 



which, it is important to notice, is the same for all values of a. 



Throughout this discussion the technical term " probable error" has 

 been used ; it may in every instance be replaced by Mr. Galton's very 

 apt name " quartile," in which case the results of these problems may 

 be read in conjunction with Mr. Galton's papers. 



