26 
BULLETIN OF THE BUREAU OF FISHERT5S 
great abundance the carrying capacity of the boat limits the size of catch so that above 
a certain point it is impossible to measure the variations in abundance. (See fig. 11.) 
In Table 3 is given the daily catches of the four largest and four smallest purse-seine 
boats operating during 1929. It is obvious from the table that the average size of 
catch would tend to rise with an increase in the size of the vessels, tending to minimize 
any fall due to depletion, because the larger the boat the higher the level at which the 
curve of catch is truncated. 
Another important factor to be considered is the shift in the fishing grounds. 
On new grounds the average size of catch may be expected to be larger than on older 
grounds. Thus the constant shift of the fishery to new grounds as the older are 
depleted has kept up the average size of catch, obscuring and minimizing any fall in 
abundance. For these various reasons any decline shown by this method must be 
regarded as a minimum decrease and can not be regarded as showing the actual extent 
of depletion. 
Table 3. — Frequency distributions of catches of the four smallest and the four largest purse-seine 
vessels of fleet in 1929 
In determining the general abundance by the average size of the deliveries a 
standard average delivery for each date was obtained by the formula: 
oti "H &2 + . . . . + ct n 
s = f 
n 
in which a it a 2 , etc., are the arithmetic means of the deliveries on the given date in 
different years and n is the number of years. A standard curve was then obtained 
by smoothing these standard averages by threes, thus obtaining a smoothed average 
for each date, designated by S, Si, S 2 , etc. 
Each month in each year was next compared with that month’s portion of the 
standard curve by the formula : 
, „ (log a -log S) + (log cti — log Si) + . . . + Qog a N — log S N ) 
log u 
