qn 
From time to time information given to newspapers told of these 
experiments and requested the cooperation of hook-and-line and com- 
mercial fishermen, 
The numbers of fishes tagged are summarized by kinds and 
streams in Table II, p. 6. The number of returns of tags from the 
different kinds are summarized in Table III, p. 7. Hook-and-line 
fishermen returned 45 tags, commercial fishermen 31 tags, while 47 
tagged fishes were recaptured in our own nets after one, two, or at 
most a few days. The maximum and average periods that tags were borne 
by the different kinds are also given in Table III. Tabulated details 
of the history of each tagged fish whose capture was reported are 
given in Table IV, pp. 8-16. 
Grateful acknowledgments are due those anglers and commer- 
cial fishermen who furnished the data on which this report is based. 
In all parts of the state the field work has been greatly facilitated 
by commercial fishermen who have given freely of their intimate know- 
ledge of Illinois waters, fish life, and fishing methods. I wish to 
thank the people who have made up the field parties of the Natural 
History Survey during these different seasons of field work and 
especially Mr. Francis D. Hunt, who has been in immediate charge of 
these parties, 
Soon after the reports on the place and date of capture of 
tagged fishes began to accumulate, it was obvious that the shortest 
water distance from the place the fishes were released to the place 
where they were retaken was not proportional to the length of time 
they were free. The longer the time the smaller was the average 
daily distance traveled. 
By watching the movements of fishes in clear waters it 
appears that there is at least some degree of randomness. In casting 
about for some method of measuring this degree of randomness, it was 
found convenient to compare the movements of fishes with the.movements 
of Brownian particles in a liquid, since the latter seem to typify a 
movement entirely random in nature. The rate of movement of Brownian 
particles has been expressed in a series of equations by Frofessor 
Albert Einstein. Briefly, these equations state that the distance of 
&@ Brownian particle from the starting point is, on the average, pro- 
portional to the square root of the time. By applying this measure of 
randomness of movement to fishes it may readily be ascertained whether 
or not fishes exhibit a sort of “homing instinct," or whether they 
tend to swim in certain directions, 
For each fish, the shortest water distance in miles has 
been divided by the square root of the number of days the tag was 
carried. This gives an expression of the number of miles, or fraction 
of a mile, that this fish may be expected to be distant after one day. 
Such numbers for different fishes are weighted by the number of days 
the tags were carried and averaged in various ways to give what may 
be called migation constants, These migration constants may be 
defined as é calculated average distance in miles away from the 
starting point after one day of time. 
