106 Prof. F. Y. Edgeworth's Exercises 



with attention if necessary to their sign. Thus, e, e v e 2 being 

 the moduli of independent errors, 



e x plus e 2 = s/e^ + e*?, 



ex minus £ 2 = V ' e± -i~e 2 9 . 



But (e x plus \e) plus (e 2 minus fie) 



To exemplify the combination of the errors with which p is 

 affected, let us select out of the methods comprised under 

 heading (/3) that which is most easily handled, namely, the 

 uncorrected form of /3(2) ((i.)) ; according to which Sy-f-S.2? 

 is put for p 12 , the summation extending from positive to 

 negative infinity. Since the ordinate of the centre from 

 which the y's are measured is liable to the error '77-h sjn *, 

 Sy is liable to the error *77 x *Jn. By parity S# is liable 

 to the error '77 x \/n. Also S# = w -f- s/ir (nearly) = S# 

 (nearly) ; since each set of observations ranges under a 

 probability-curve of which the modulus is unity. Accord- 

 ingly the error of p 12 derived from source (a) 



= c5- error By minus /C) xo error So? 



_ r58 7r -58 77-11 

 [_ n n J 



To this is to be superadded the error from source (ft) f; 



V 



(2'16-p 12 2 )7T 



An illustration of this reasoning is afforded by the computa- 

 tion of correlation % between stature, cubit, and knee-height, 

 referred to in the Philosophical Magazine for December 

 1892, p. 523, note. There different values were obtained 

 for each p, according as the positive or the negative devi- 

 ations were operated on ; and according as the formula used 

 for p was Sy-i-Sa? (as being taken as " subject,' ; and y 

 relative §) or S#-i-Sy (vice versa). 



* Above, p. 100. f Above, p. 101. 



X The statistical materials were supplied by Mr. Francis Galton, F.R.S. 

 and the arithmetical work by Mrs. Bryant, D.Sc. 

 § Above, p. 100. 



