Ethel M. Eldekton and Karl Pearson 
499 
round zero in the required manner. The interest of this test is that we see that 
the bulk of the time effect has been removed even when we reach the second 
difference, a result confirmed by the fact that the correlation of the deathrates' 
second differences is in every case already substantially negative. 
(iii) A third set of tests are those which are based on the standard deviations 
of the differences. In the first place if we assume steadiness to have set in, we 
can calculate a-^, the intrinsic standard deviation from the known value of ,., by 
means of Dr Anderson's formula cited above (p. 496). Table VI gives the intrinsic 
values of a^, i-e. o-y as deduced from the variability of the differences. It will be 
at once observed that for the third difference the mortality ratios of the third, 
fourth and fifth years of life I'each steady standard deviations. In the case of the 
first year of life it is not till the eighth difference that this result is reached, while 
in the case of the second year, it can hardly be said to have been obtained with 
the ninth difference. A distinction should be noted here of which the exact 
physical significance is not obvious to us. In the second, third and fourth years 
the intrinsic standard deviations fall to steady values, but in the first and second 
years they rise towards those values and these are just the cases where steady 
values are not absolutely reached. 
TABLE VI. 
Intrinsic Standard Deviations (o-v). 
Year: 0 
-1 (mi) 
Year: 1 
-2 (m.) 
Year: 2 
-3 
Y'ear: 3 
-4 (^4) 
Year: 4 
—5 (ills) 
Order of 
Difference 
6 
? 
6 
? 
6 
? 
6 
? 
6 
? 
1st 
7-62 
6-96 
3-90 
3-86 
1-75 
1-83 
1-53 
1-52 
] -23 
ro9 
2nd 
7-89 
7-22 
4-13 
4-09 
1-67 
1-81 
1-29 
1-34 
1-00 
•83 
3rd 
8-14 
7-45 
4-32 
4-28 
1-62 
1-78 
1-21 
1-29 
•93 
•80 
4th 
8-34 
7-63 
4-47 
4-42 
1-59 
1-76 
1-18 
1-29 
•87 
•77 
5th 
8-50 
7-76 
4-60 
4-54 
. 1-.58 
1-76 
1-17 
1-28 
•86 
•77 
6th 
8'61 
7-83 
4-71 
4-63 
1-59 
1-77 
1-17 
1-28 
•86 
•78 
7th 
8-66 
7-84 
4-80 
4-72 
8th 
8 -08 
7-85 
4-88 
4-78 
9th 
4-97 
4-82 
(iv) There is another test for the standard deviations of the differences 
deduced by Cave and Pearson from the Andersonian results and used by tbem in 
their memoir on Italian Index Values*, namely as steadiness is approached the 
ratio of the squares of standard deviation of successive differences should approach 
closer and closer to 4, the exact value being 
* Biometrika, Vol, x. p. 346. 
Biometrika x 64 
