436 
PROFESSOR K, PEARSOX AXD MISS A. LEE OX THE DISTRIBUTIOX 
The following are some of the formulae given in the memoir above referred to ; 
Probable error of mean 
Probable error of y . 
. = ‘67449cr. \/n, 
•674497 /PTS 
• “ V ^ S 
Probable error of p . . = ‘&7449pj\/n'6, 
Probable error of ?/q thej 
modal frequency ) 
Probable error of y-^ the] 
mean frequency J 
•6i'449?,/o / 
^■Z,i At + S’ 
■ 674497 , ^ 
\/'4n 
1 + 
Probable error of o- . . = 6<4^g- / 
k/Z)i V 
1 
Probable error of skew¬ 
ness 
^ (y + l)-bS’ 
•67449 ^ 1 
2v/?i y 4-4 vt(_p + 1)S’ 
p + 1 
Correlation of errors in and y 
1 
T^’ 
Correlation of errors in p and mean = 0, 
Correlation of errors in y and mean = 
%/.3 
1 s/(i-hS). 
Here S is the series 
and T 
P 
B. ^ P. 
IT 
Bi 
2p 
42j'’ 
the B’s being the Bernoulli numbers. 
Now a consideration of these formulae gives the following results—which will be 
found to be fully verified by the Table Y, of calculated values— 
(rt.) The errors in the mean, standard deviation and skewness are very small The 
errors in both mean and modal frequencies are small, but the error in the modal 
frequency is considerably smaller than that in the mean frequency. This follows 
from the fact that the frequency curve is horizontal at the mode, but slopes at the 
mean, and accordingly any bodily shift of the curve produces far more efiect on the 
mean than on the modal frequency. 
(6.) The errors in_2t and y are large in some cases very large. The question then 
arises how is it possible to determine the frequency ciu’ve correctly. The answer lies 
in the fact that p and y are so highly correlated, that given a large error in p, there 
