271 
1910-11.] Mathematical Theory of Eandom Migration. 
Those for higher values of n may be obtained by differentiating the above 
values with respect to i 2 . 
(3) To find k and c from the moments is easy, but for convenience a 
k 
table is given by which the values of — may be obtained when the value 
of i.e. -i- has been calculated, 
b 6 /u 2 2 
Table showing the values of - for different values of 
k l + ? + A 
c 4 3 c 2 15_1>4 1 q 
/r 4 , 4 k 2 4 6 /* 2 2 ~ 6^ 2 
c 4 + 3 c 2 + 9 
k 
1 
c 
6 S - 
Differences. 
*50 
•4314 
227 
"55 
•4541 
230 
•60 
•4771 
232 
*65 
•5003 
230 
•70 
•5233 
226 
•75 
•5459 
222 
•80 
•5679 
213 
•85 
•5892 
205 
•90 
•6097 
196 
•95 
•6293 
185 
1-00 
•6478 
346 
1*10 
•6826 
310 
1*20 
•7136 
275 
1-30 
•7411 
244 
1-40 
•7655 
216 
1-50 
•7871 
(4) A special case arises in random migration if the area to be invaded 
is bounded by a straight boundary on the one side of which there is an 
infinite field uniformly stocked with the organism which is migrating. In 
the case of animals actually migrating this form has been found by Pro- 
