X.—CORRELATION : ILLUSTRATIONS AND METHODS. 197 
harvest are themselves very largely dependent on the weather, 
and consequently, on an average of many years, the limits of 
the critical period will not be very well defined. If, therefore, 
we correlate the produce of the crop (X) with the characteristics 
of the weather (¥) during successive tervals of the year, it 
will be as well not to make these intervals too short. It was 
accordingly decided to take successive groups of 8 weeks, over- 
lapping each other by 4 weeks, 7.e. weeks 1-8, 5-12, ete. 
Correlation coefficients were thus obtained at 4-weeks intervals, 
but based on 8 weeks’ weather. 
13. It remains to be decided what characteristics of the weather 
are to be taken into account. The rainfall is clearly one factor 
of great importance, temperature is another, and these two will 
afford quite enough labour for a first investigation. The weekly 
rainfalls were averaged for eight stations within the area, and 
the average taken as the first characteristic of the weather. 
Temperatures were taken from the records of the same stations. 
The average temperatures, however, do not give quite the sort 
of information that is required: at temperatures below a certain 
limit (about 42° Fahr.) there is very little growth, and the 
growth increases in rapidity as the temperature rises above this 
point (within limits). It was therefore decided to utilise the 
figures for “accumulated temperatures above 42° Fahr.” i.e. 
the total number of day-degrees above 42° during each of the 
8-weekly periods, as the second characteristic of the weather ; 
these “accumulated temperatures,” moreover, show much larger 
variations than mean temperatures. 
The student should refer to the original for the full dis- 
cussion as to data. The method of treating the correlations 
between three variables, based on the three possible correlations 
between them, is described in Chapter XII. 
14. Problems of a somewhat special kind arise when dealing 
with the relations between simultaneous values of two variables 
which have been observed during a considerable period of time, 
for the more rapid movements will often exhibit a fairly close 
consilience, while the slower changes show no similarity. The two 
following examples will serve as illustrations of two methods which 
are generally applicable to such cases. 
Hlustration iv.—Fig. 41 exhibits the movements of (1) the 
infantile mortality (deaths of infants under 1 year of age per 1000 
births in the same year) ; (2) the general mortality (deaths at all 
ages per 1000 living) in England and Wales during the period 
1838-1904. A very cursory inspection of the figure shows that 
when the infantile mortality rose from one year to the next 
the general mortality also rose, as a rule; and similarly, when the