t= AXIS OF TIME IN HOURS 



DRIVING PATH 

 CONSTANT SPEED 



>-X = AXIS OF DISTANCE 



Lj+I — 



Figure 12, Fishing situation in L^ during the census hour. 



Each verticle line represents a fisherman. The position of the line 

 along the X-axis (of distance) establishes the fisherman's location, and 

 its position and length relative to the t-axis (of time) establish the 

 time interval that the man fishes. The number of individual lines which 

 extend within the rectangle constitute f^i- The number of intersections 

 of the diagonal driving path (idealized to be a path of constant speed) 



with the verticle lines is our count k 



ii* 



must lie within the indicated rectangle. 



Clearly, these intersections 



In the case of the Yellowstone Lake census, T ■ 1 (hour). In 

 certain cases, however, it might be necessary or advisable to consider 

 a frequency histogram (complete census) divided into cells of width T 

 (hours) each; hence the general treatment is presented, here. 



by. 



The probability "p" of observing the "average" fisherman is given 



(8) 



f. 



11 



and it is this expression which we wish to evaluate. 



Suppose the k*"^ fisherman contributes t^ hours of effort 

 (k - 1, 2, ..., f^3^). Let us replace Figurel* by an idealized situati<^ 

 where each of the f^-^ fishermen fish the same expected time E(tjj) » E(t). 

 This gives us Figure 23 • 



39 



