267 
1910—11.] Mathematical Theory of Random Migration, 
the average flight. Now, if <x vary from 0 to oo for a first approximation, 
_ c r 
its frequency might be represented by type iii. or, say, y = cr n e k , in which 
case the migration form would be 
I (jW'2^ o' 2 
2-7T JO 
_ cr 2 
This form is very intractable as a working integral, and as <r 2n e * 2 gives 
a somewhat similar series of curves, the latter may be substituted with 
much simplification of the calculation, so that the distribution of a species 
might be represented by 
c [ cr 2n+2 e 
Jo 
a ; 2 <r- 
0-2 k2 d(T, 
a form easily reducible for any value of n. This is the same surface 
