Worlund of the Fish and Wildlife Service jfor 

 their helpful comments. 



DEFINITION OF TIME SPENT 

 IN A FISHWAY 



It is difficult to record the time 

 spent by an individual fish when even a 

 small group is present in a fishway. How- 

 ever, under appropriate conditions one can 

 record the numbers passing two (or more) 

 points in successive units of time. If one 

 does this at the entrance and exit (or amy 

 other locations of interest), he may calcu- 

 late an average time of entry and an aver- 

 age time of exit. The difference between 

 these averages is then a measure of the 

 average time spent in the fishway by the 

 individuals of the group. 



Two such averages, the mean and the 

 median elapsed time, have been used by 

 Elling and Raymond (1959). Of course, both 

 may be derived without regard to the order 

 in which particular fish enter and leave. 

 One may compute the median as soon as half 

 of the number of fish entering is recorded 

 at the exit. However, since individual 

 times of entry and exit are not recorded, 

 the observed euid true medians will differ 

 by some unknown amount. The observed mean, 

 on the other hand, will be identical with 

 the true mean unless a test is stopped 

 before all fish have passed through the 

 fishway. 



In practice, some fraction of those 

 entering usually fail to leave in a reason- 

 able time. When this fraction is large, 

 unfavorable conditions exist for fish pas- 

 sage and such information is essential for 

 planning new fishway designs. To avoid 

 waiting for a few fish and thus to permit 

 reasonable scheduling, Elling juid Raymond 

 (1959) terminated most tests before all 

 entering fish had passed through the fish- 

 way. The fact that their observed means 

 and medians differed only slightly in tests 

 not terminated before all fish had left 

 suggests, at least for the limited scope of 

 their operation, that this procedure was 

 reasonable. 



In what follows we shall use the term 

 "average" time. It will make no difference 

 to the concept of capacity whether this 

 average is the mean or the median. 



DEFINITION OF DELAY 



The idea of capacity implies that the 

 average time spent in a fishway by indivi- 

 duals is some function of the number of 

 fish present. For example, Pretious, Kersey 

 and Contractor (1957) state: "It is known 

 from experience with the salmon runs on the 

 Eraser River that the crowding of fish in a 

 limited area reduces freedom of movement 

 and slows down the migration of fish. Thus, 

 if the fishway design capacity (in numbers 

 of fish) were to be exceeded, it could be 

 expected that the numbers of fish passing 

 through the fishway per unit time would 

 diminish rather than increase during the 

 time that the fislMay was overcrowded." 



The actual relationship between aver- 

 age time and the number present could be of 

 various types. For example, average time 

 might be less at a moderate than at a low 

 number present. 



But for the present let us postulate 

 the situation of figure 1. Here, the in- 



Average Number Present (N) 



Figure 1. — Hypothetical relationship between 



average time and average number present. 



crease in T related to a particular N is 

 given by the vertical difference between 

 any T, N coordinate and the dashed line. 

 For the moment we shall apply the term 

 "delay" to such differences. 



