277 
1910-11.] Mathematical Theory of Random Migration. 
Where this theory fails, however, is in its application to seasonable 
epidemics such as enteric fever when averaged over a number of years. 
This might be expected. Though the hypothesis that the infectious 
organism is given out for a definite time at a constant rate may he 
sufficiently accurate when applied to a single epidemic, it can hardly be 
expected to hold when an average of years is considered. An early or a 
late epidemic of the disease is the product of special weather conditions 
which will occur very seldom. So that though the epidemics occurring at 
the usual time will tend to have their irregularities smoothed, the beginning 
and the end of the compound curve will be framed on a different law from 
the middle. An endeavour has been made to frame an approximate formula 
to meet this, but none has been found fitting the facts. 
To test the likelihood of a curve fitting, Professor Pearson’s method is 
used throughout. To do this the actual and theoretical numbers are differ- 
enced, the difference squared and divided by the corresponding theoretical 
number. These are summed. The sum is denoted by x 2 - The table for 
testing curve fitting * is then consulted, and the value of P obtained. 
Thus if P = *8 it signifies that in testing the matter over again a worse fit 
might be expected eight times out of ten, so the fit is good. The opposite 
interpretation is given when P is small, say == ' 2 , when a worse fit might 
be expected only in two out of ten trials. 
Plague in Hong-Kong. 
The epidemics of plague in Hong-Kong are typical of the great majority 
in all the East. They are nearly bilaterally symmetrical ; they spring from 
Table showing the Number of Plague Cases, Actual and Theoretical, in 
the Epidemics of Plague in Hong-Kong in 1902 and 1904. 
1902. 
Number of Cases. 
1904. 
Number of Cases. 
Actual. 
Theoretical. 
Actual. 
Actual Figures cor- 
rected so as to 
correspond with 
the Mean. 
Theoretical. 
March 
2 
3-8 
4 
3-6 
7-0 
April . 
27 
38-5 
40 
34-4 
35 
May . 
157 
147-0 
135 
122-0 
126-4 
June . 
194 
178-7 
194 
186-0 
180-5 
July . 
131 
147-0 
96 
109-2 
126-4 
August 
50 
38-5 
19 
29-3 
35-1 
September . 
2 
3-8 
9 
11-3 
7-0 
* Biometrika, vol. i. p. 155. 
