From tire to time information «<iven to newspapers told of these 
exoeriments anc requested the cooperation ol hookesind-line ana 
commercial fishermon. 
The numbers of fishes tepred ere surrarized by kinds 
and streams in Table Ili, p. 6 The number of returns of tags 
from the ciffercent kinds are summerized in Table IIu, p. 7%. ook- 
and-line fishermen returned 40 tags, commercial fishermen 51 
tags, wnile 47 tagged fiskes were recaptured in our own nets 
efter one, two, or at most a few days. . Tre maximum and average 
periods thet tags were borne by the different kinds are also 
given in Table TI1. Tabulated details of the history of each 
taggec fish whose capture was reported are given in Table IV,pp.8-16. 
Grateful acknowledgments ere cue those anglers and 
commercial fishermen who furnished the date on which this report 
is based. In all parts of the state the fielc work has been 
sreatly facilitated by commercial fishermen wro have given frecly 
of their intimate knowledge of Illinois weters, fish life, and 
fishing methocs. i wish to thank the people who have made uy the 
field parties of the Natural Fistory Survey during these differ- 
ent seasons of field work and especially lir. 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 apoears that there is at least some Ccegree of randomness. In 
casting about for some method of measuring this degree of random- 
ness, it was found convenient to compare tne 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 mover.ent of Brownian particles has been expressed in a 
series of equations by Professor Albert Hinstein. Briefly, these 
equations state that the distarce of a Brownian particle from the 
starting point is, on the average, proportional to the square root 
of the time. By epolying this measure of randomness of moverent 
to fishes it may readily be ascertained wnether or not fishes 
exhibit a sort of "homing instinct," or whether they tend to swin 
in certain directions. 
For each fish, the shortest water distence 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 sre weighted by 
the numbcr of days the tags were carricd and avereged in verious 
ways to give what may be called composite migration constants. 
These migration constants rey be defined as the calculated average 
distance in miles awav from the starting point after one day of time. 
