( 22 ) 

 and JA< and .\f,, donote tlip principal axes of probability, so that: 



The mean crroi-, thei-oforc, ciin be fak-nlated without any knowledge 

 of the situation of the j)i-ineipal axes, when the mean error of the 

 components relative to arbitrary rectangular axes is known. 



If F is independent of <9 : 



M 



[72 



M^ = Jf„ = 



or, putting: 



■ ± = n' 



F=-e-J^Y- (5) 



The specilic probability of an error, inde[>endent of the direction, is : 



I- 



(J e-i''r dtp = 2 h' Q e-J''r^ (6) 









From this it ajjjiears that the |)r()babilily of an error zero is not, 

 as in the case of linear errors, a niaxiiunni, but a niininiuin, that 

 the cHr\e of the spec. prob. (G) (gi\en in ScnoLs' paper) shews a 

 maximum for the \ aluc of tj: 



o,n = —-Af[/2 (7) 



and, also, that the computation of the jn'obable error will lead to a 

 coefticicMit of .]/ considerably dilferent from that found for linear errors. 

 We have then to ask for what \alue r of o : 



J- ^2 



I» 



7' = ().8325G J/ (8) 



This \alue of the coefficient of the probable error, considerably 

 greater than is found for linear errors, ().G745, clearly shows that 

 and to what degree results, obtained in investigations of this kind, have 

 to be put to an unusual severe test, and also that there is some 

 reason to adhere to tiie use of the ))robablc eri'or, which of late 

 years has been somewhat neglected, 



A reduction of the mean error has no sense if this reduction is 



