210 TRANSACTIONS LIVERPOOL BIOLOGICAL SOCIETY. 
Tyrer IV, that is 
A 
Y=Yo (1+ 5) 
The limiting form of Type I is a curve which is 
symmetrical but limited in both directions. We do not 
x 
— m —yp tan-1 — 
é a 
often find such distributions among plaice catches, and 
none of the series analysed falls into this group. Instead 
of such a type we find the above one where the curve 1s 
asymmetrical and has branches extending to infinity in 
either direction. The natural conditions giving such 
a distribution are the presence on the fishing ground of 
plaice with a considerable range of sizes; and the partial 
choking of the meshes of the net with sea-weed and other 
débris. Some of the smaller fish which would otherwise 
escape are thus caught; on the other hand, the larger 
fish are able to swim out from the net because of the 
decreased draught of water through its meshes— 
obviously the smaller fish are not so able to do this. In 
a catch of this kind one cannot deduce the range of 
lengths of the fish forming the population sampled by 
the net, and the calculation of a standard deviation would 
probably be attended by a larger e error than the statistical 
method would indicate. a 
The table on the foHowing page represents the 
theoretical distribution of. lengths in. several catches 
(1,593 fish) of plaice made in Barrow Channel in June, 
1910, by a second-class sailing vessel employing a trawl- 
net of 6-inch mesh. It will be noticed that the fre- 
quencies are not tabulated for equidistant values of 2, 
the reason being that—to avoid labour—the equation was 
put in the form 
(xz =atan@ 
| y=y cos’ 7.0.e 
and arbitrary values of the argument were rae chosen. 
The chart on p. 212 (Fig. 2) represents both the original 
