OF ERRORS OF JUDGMENT AND ON THE PERSONAL EQUATION. 
277 
) 
= (^6 — H-3^ + 9/^/ — 
= (^8 - P -/ + 16 /^ 3 Vs — 8 / A 5 ^ 3)/?1 
^M 2 l“3 “ Vs ^ A'-g/^s)/^^ 
— S/io/Xg — + \2ix/tx^)ln 
= (/Xg — J/Xg® — /Xo/X.t)/« ^ 
«> 
For the special case of the normal curve, since 
ju-j, = S/Xj^ = 3a-^, Pq = ISo-’’, /xg = 105 (t® 
H = H-o = H^s =0, 
we have:— 
Probable error of /Xg = '67449 X .(xxiii.). 
,, ,, P '3 = '67449 X .yQcT^iyn .(xxiv.). 
,, ,, H-i— '67449 X Y/9f>o-V'\/^.(xxv.). 
= 9 . . (xxvi.). = 0 . . (xxvii.). = lys . . (xxviii.). 
In a further memoir on skew variation,^ not yet published, I show that if the 
differential equation to the frequency curve be 
1 chj cIq + «,« , . , 
y clx P h^x + ^ 
then whatever be the form of the curve, the distance d between the mean and the 
mode, and the skewness are always given by 
P3(P4 + _ 1 \/P2 \/A f^3 -+ 3) 
2 ~ 2 5^2 - 6^1 - 9 
_ Ps fp-t + S/X^") _ _ \/A (/^2 + 9) 
2y/ yU.o — 6 /X 3 ® — O/Zj®) ^ SySj — 6/3j — 9 
(xxx.). 
(xxxi.). 
* My original memoir (‘ Phil. Trans.,’ A, vol. 186, p. 343), being much misunderstood, has been 
alternately over- and under-rated. I had found that the ordinary theory of errors was far from 
describing frequencies within the limits of error imposed by a random sampling. My object was then to 
discover a series of curves which would enable me in a very great number of cases to do this. I did not 
select these curves at random, but endeavoured to see where the usual hypotheses failed and must be 
generalised. My hypergeometrical series was not empirically chosen, but on the grounds of the axioms 
(a), (13), (y) above. I chose a system where the positive and negative errors were not equally probable, 
where there was not an infinite number of cause-groups, and lastly, one where these cause-groups did not 
contribute independent but correlated elements to the total error. All these points as well as criticisms, 
mostly due to complete misunderstanding of what random sampling means, I have considered in a 
further memoir. 
