Eleanor Pairman and Karl Pearson 
257 
We now turn to the abruptness coefficients at the end of the first year of life 
and find : 
Males 
Females 
«, = 9626, and liy (xxxii) 
)i,j = 9543, and by (xxxii) 
374«,'=- 808-283,5789 
457ffli'=- 942-176,2334 
Ha =129 
374a./ = 3203-044,5476 
7(2=204 
457«2'= 3281-101,5644 
W3 = 61 
374«:,'= - 9271-066,1366 
«:i = 57 
457a3'= - 8958-636,6700 
«4 = 27 
374«4'= 23389-468,5164 
?i4 = 49 
457a4'= 22229-438,8090 
^5=14 
374a,/= -69671 015,1599 
?i,r, = 25 
4570.5'= -66617-544,9906 
374 X jV 
(«i'-6V«3'+2ifVo«s')= - 56-784,418, 
457 X iV («] 
' - ff 0 «3' + 2 0 0 = - 68-275,090, 
3 
74 X (a/ - if (f«4') = 18-962,592. 
457 
X rio («2' - if (T«4') = 19-991 ,508. 
Thus : 
374^/"= 2600-215,572, 
374ft2"' = "^077-37O,741. 
Thus : 
457/xi"'= 2527-224,90-1, 
457/x2"' = 76222-175,159. 
From (xxxi) we have : 
From (xxx 
i ) we have : 
9626,x,"= - 7768-448,082, 
9.54.3/xi"= - 7640-738,2653, 
or, 
l-/ii" = -]930, 
9626/x2" = 6736-839,298. ■ 
or, 
l-;x," = -]993, 
9543/H2" = 6604-373,5073. 
Thus : 
10,000|Ui'= -5168-232,510, 
Thus : 
10,0(Hy,'= -5113-513,361, 
and 
^,'= --516,823; 
10,000/^2' = 77814-2 10,039, 
;li,/ = 7-781,421 ; 
and 
ixi = - -511,3513 ; 
1 0,000/i2' = 82826 -548,666, 
,X2' = 8-282,655 ; 
or, finally 
Mean = -4832 year. 
Standard Deviation = 2-7412 years. 
or, finally 
Mean = -4886 year. 
Standard Deviation = 2-8322 years. 
It is clear that in both cases the centring of those who die in the first year of 
life is a little under 0-2, instead of slightly over 0-2 as in the English data. It is 
worth while inquiring what the effect of concentrating the deaths in the first year 
of life at 0"2 and then simply determining the crude moments will be. We find : 
Concentration at 0-2 
Concentration at 
actual centres* 
Complete corrections 
Male 
Female 
Male 
Female 
Male 
Female 
Mean 
Standard Deviation 
-496 
2-729 
•496 
2-821 
•489 
2^730 
•495 
2^822 
•483 
2-741 
-489 
2-832 
This process then gives quite a reasonable value for the mean and standard 
deviation. Thus all we have to do for a rough practical value is to use the /i,/' of 
the first equation of (xxxi) to obtain the centring of the first group and then find 
the raw moments only. For a very high first group this is considerably better 
than applying our first non-asymptotic method and of course better than mere raw 
moments. The following are values found from year groups : 
* That is at -1930 and -1993. 
