448 PROFESSOR K PEARSON AND MISS A. LEE ON THE DISTRIBUTION 
A.n ©xaixiiUcition of these lists seems to show that, even allowing for some dis- 
tnrbances in the Stony hurst, Llandudno, and Margate returns, there is no 
geographical fact closely represented by range above the mode thus measured. 
There are but few and small changes introduced into the order of stations, whether 
we consider or only. But differs so widely from that we must 
consider one or other of them as of little value in the determination of the nature 
of the frequency above the mode. In general the range above the mode dealt with 
in this manner appears to be more closely correlated with local conditions than with 
geographical position. 
It would undoubtedly be most satisfactory in order to appreciate the skewness 
of the range of frequency to calculate the values of the standard deviation Lora the 
mode for the two portions of the frequency curve, which fall respectively above and 
below the mean. The extremely slow convergence, however, of the series which 
express incomplete F-functions, renders this calculation extremely tedious, and such 
mechanical methods as Amsler’s Integrator do not, in our experience, give very 
good results,"*^ v/hen the curves for which the second moment is to be found have, as is 
the case with nearly all frequency-curves, considerable “ tails.” 
Fortunately, Mr. De Forrest, in a paper published in the * Analyst’ (vol. 10, p. 69; 
Iowa, 1883), has found for a series of values of p the probable deviations in excess 
and defect of the mode, i.e., the values of x on either side of the mode for which the 
corresponding verticals, y, cut off the half areas. Unfortunately, although he has 
interpolated for a considerable number of values of p, his values of the probable 
errors are only calculated for the small series p = 4, 5, 7, 10, 20, 50, and 200, doubt¬ 
less on account of the great amount of arithmetic involved. Accordingly his table is 
only as strong as these seven values, which are as follows :— 
De Forrest’s Table of Probable Deviations. 
tq = probable deviation in excess of mode, i.e., along negative x. 
^3 = ,, defect ,, ,, positive ,, 
p- 
— yej. 
yen. 
4 
0-822 
1-613 
6 
0-955 
1-788 
7 
1-289 
2-085 1 
10 
1-654 
2-450 
20 
2-561 
3-359 1 
50. 
4-334 
5-133 ; 
200 
9-121 
9-920 
The completion of the Table would undoubtedly be a useful, if laborious, piece of 
work. 
We have calculated the values of e^ and for the twenty stations by interpolation 
[* All Amsler’s Integrator, especially constructed for me, to determine /ioj /.u is fairly satis¬ 
factory for “oval ” sections; it gives a passable value of /ij, but is not accurate enongb to give working 
values of and /'.j for “tailed ’’ areas.—K.P.] 
