James Henderson 
177 
of the values of the series than a set of isolated points would. Figures 1 — 7 corre- 
spond to the data given in Tables I — VII. 
Now in the case of the Incomplete F-function we obtained two expansions, with 
respect to the mean and the mode respectively, and the graphs tell us which of 
these two gives us the better approximation. Figs. 1 and 3 (Tables I and III) 
show the variations in the values of the series for ^ .^,dx from the mean 
r(49) 
and the mode respectively, while Figs. 2 and 4 give us similar information fir 
OOiOO 
l-J I I I I I I II T — r 
Ml-a)T3 \ % \ T? \ S '•'lO % Tl2 Us \H 115 fl6 \l fl8 T19 fjO ^21 % % \\ \i \b \i % Tjo 
NUMBER OF TERMS 
FiK. 1. 
•16100 
•16000 
•15500 
z(,l-ti)T3 
'5 '6 '7 '8 '9 '10 '11 
\2 % T14. T,5 T,7 Ijg \^ T20 \\ T22 1^3 T24. 125 "^Zb "^11 ts \^ \o 
NUMBER OF TERMS 
Fig. 2. 
It will be seen that in Fig. 1 the points are much closer to the ' true value ' 
line than in Fig. 3 (and .similarly in Fig. 2 they are closer than in Fig. 4) so that 
the expansion from the mean seems to give a better approximation than that 
from the mode and it has the additional advantage that the terms in Ti and t._> are 
missing. Besides, it seems more natural to expand these normal curve functions in 
terms of the mean and standard deviation. For comparison purposes the graphs are 
all on the same scale. The graphs for the mode and the mean behave in a very 
Biometrika xiv 12 
