Eleanor Pairman and Karl Pearson 
249 
The month subranges will be quite adequate at the childhood terminal. 
As the results are based on 1877 — 1881 averages, we shall suppose the month 
to be 30-4375 days. Thus hjK = 10-145,833, hjhp = 1. We find 
= -0924,8936, 
a, = --1877,2637, 
«/ = _ r904,640. 
J? 2' 
= -0333,4685, 
a., = -2966,9657, 
a.; = 30^541,331, 
= -0399,8581, 
a, = - -3909,0057, 
a,' = - 408^253,057, 
n,' 
= -0286,3369, 
a,= -3117,2715, 
= 3303-128,589, 
>h' 
= -0294,9524, 
a, = --1139,7730, 
a,' = - 12253-408,881 ; 
n'p-i 
= •0471,3156, W = 
-035,759, 
^ p—S 
= -0442,9353, 6./ = 
b,= 
- -004,823, 
= -0420,1297, W = 
hs = 
-013,861, 
= -0380,6000, 6/ = 
64 = 
- -012,670, 
n'p 
= •0351,7130, 6/ = 
h = 
-004,967. 
From these we deduce 
tV(«i'-6V«3' + ^J,o«;)= -003,093, ^(b^-^W+^i^,W}^ -002,961, 
jh K - tI 6 0 = - •«37,793, (6; - jI^W) = - -000,036, 
whence Total abruptness correction on 1^/ = -006,054, 
= -843,679. 
Thus = 3-765,278 months, fi.: = 26-570,147 (months)-, 
using of course Sheppard's correction. 
Finally we reach 
Mean = 114-61 days as against* 113^07 days. 
Standard Deviation = 107-15 „ „ 105-44 „ 
obtained from taking the raw moments of small elements of one day up to the end 
of the first fortnight. Thus, if we desire to get a mean within 1-5 of the correct 
value, it will be well to adopt abruptness corrections. 
(10) Illustration IV. In view of the fact that in the previous illustration the 
infantile death-rate curve has probably an infinite initial ordinate it seems well to 
measure, in a case which can be tested, the degree with which our corrections give 
the actual values of the moment-coefficients in such a case. 
We choose the curve y — \x ^, 
and suppose ten subranges going up to the terminal x = 10, from x = 0. 
* Pearl's results modified by taking the average month to be 30-4375, not 30 days. 
Biometrika xii 17 
