Eleanor Pairman and Karl Pearson 255 
Assuming the legitimacy for the present purposes of this redistribution in year 
groups we find for moments round the end of the first year of life : 
Males , Females 
1238i//" = 9446 1247;'/" = 12079-5 
1238^;" = 207,007-25 1247ia/" = 331545-75 
Again we have for males : 
n, = 8762, and by (xxxii) «/ x 1238 = - 1122-222,8440, 
«, = 393, a,' X 1238 = 3041-534,5373, 
V, = 140, X 1238 = - 9518-206,0741, 
??4 = 95, (//< 1238 = 19254-345,0950, . 
n, = 86, ' a/ x 1238 = - 58196-492,8841. 
Our abruptness functions are thus found to be 
1238 («■' - ^T3(h + 25W«..') = - 83-056,6602, 
1238-i-i^(f/,;--,-ff.rO = 18-978,9435. 
These provide for the moments about 1 : 
1238/^/" = 9446 - 83-056,6602 = 9362-943,3398, 
1238/1*/" = 207,007-25 - 103-166,6667 - 18 978,9435 = 206885-104,3898. 
We now find from (xxxi) the values of 
8762/x/' = - 6921-345,3000, 
and 8762/*/'= 5951-033,6815. 
Thus : 10,000ya; = 8762/x/' + 1238/x/" = 2441-598,0398, 
10,000/io' = 8762/*," + 1238;*/" = 212836-138,0713, 
or /*/ = -244,160, /*/ = 21-283,614. 
- Thus finally the Mean = 1-2442 years and the Standard Deviation = 4-6069 years. 
We now turn to the female deaths and find with the same notation : 
ere 
1247 
,'/"= 12079-5, 1247zy/" = 
331,545-75. 
• 
= 8753, 1 
leading by (v) to 1247a/ = 
- 1014-250,5807, 
= 339, 
1247a/ = 
2949-801,0796, 
^^3 
= 150, 
1247fl/ = 
- 7980-615,3654, 
«4 
= 80, 
1247a/ = 
19991-399,2722, 
??5 
= 69, 
1247(// = 
- 60065-060,3135. 
