THEORY OF STATISTICS. 
infantile mortality fell, the general mortality also fell. There 
were, in fact, only five or six exceptions to this rule during the 
whole period under review. The correlation between the annual 
values of the two mortalities would nevertheless not be very high, 
as the general mortality has been falling more or less steadily since 
1875 or thereabouts, while the infantile mortality attained almost 
a record value in 1899. During a long period of time the correla- 
tion between annual values may, indeed, very well vanish, for the 
two mortalities are affected by causes which are to a large extent 
different in the two cases. To exhibit, therefore, the closeness of the 
relation between infantile and general mortality, for such causes 
as show marked changes between one year and the next, it will be 
best to proceed by correlating the annual changes, and not the annual 
values. The work would be arranged in the following form (only 
suflicient years being given to exhibit the principle of the process), 
and the correlation worked out between the figures of cols. 3 and 5. 
L. Z, 3. A OD. 
Infantile Increase or General Increase or 
Year. Mortality per Decrease from Mortality per Decrease from 
1000 Births. Year before. 1000 living. Year before. 
1838 150 > 29-4 - 
1839 151 -8 218 -06 
1840 154 +3 : 229 +11 
1841 145 -9 216 -1-3 
1842 152 | +7 217 +0°1 
1843 150 -2 21-2 -0'5 
For the period to which the diagram refers, viz. 1838-1904, the 
following constants were found by this method :— 
Infantile mortality, mean annual change — 0-21 
standard deviation 9:63 
General mortality, mean annual change — 0-09 
standard deviation 1°14 
Coefficient of correlation + 0-77. 
This is a much higher correlation than would arise from the 
mere fact that the deaths of infants form part of the general 
mortality, and consequently there must be a high correlation 
between the annual changes in the mortality of those who are over 
and under 1 year of age. (Cf. Exercises 7 and 8, Chap. XI.) 
This method, which appears to have been first used by Miss 
Cave and by Mr Hooker independently in the papers cited in 
refs. 4 and G6, has recently been generalised by “Student” and 
the theory fully developed by O. Anderson (cf. refs. 13, 14, 15). 
By taking the first differences the influence of the slower changes 
of the two variables with time may not be wholly eliminated, 
but this elimination may be mniore completely effected by pro- 
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