285 
1910-11.] Mathematical Theory of Random Migration. 
Data for the other fish are lacking with the exception of herring. The 
weekly takes at given stations afford some guide, but not much. One 
selected from the Fishery Board Report of the take of herring off Ballantrae 
is illustrated in the diagram (Diagram VII.). Here the elevation at the 
beginning of the ascent prevents accurate curve fitting, but the general 
correspondence is good. It was hoped that with the figures at a fixed 
point some better results might be obtained, and the Fishery Board very 
kindly furnished me with the figures of the weekly takes in the trammel 
nets at Ballantrae. But these figures proved insufficient to determine the 
shoal form ; in no case were the curves continuous. Factors such as the 
end of the open time, storms, etc., interfered with the returns to such an 
extent that it was not possible to use the figures.* 
* Herring catch, Ballantrae, 1903, May- August, Twenty -fifth Ann. Rep. Fish. Board Sc., 
p. 174. 
