100 THE RATE OF GROWTH OF FOOD-FISHES. 



at a length of 8 to 12 inches at the maximum age and length 

 for reproductive purposes and (3) 120,000,000 at a length of 

 6 to 8 inches which have reached the inceptive stages of repro- 

 duction, and (4) 300,000,000 immature individuals. For the 

 present purpose we may neglect the (1) and (4) and consider 

 (2) and (3). 



The effect of over-fishing is to remove the second series, 

 for apart from other reasons the members of (2) have been 

 subjected to the risks of being caught at stage (3) before 

 attaining to stage (2). 



The removal of (2) and with it (1) means that, the sup- 

 porting powers of the district remaining the same, a much 

 greater quantity of (3) and their offspring included in (4) will 

 be able to find subsistence and will survive. Hence the second 

 effect of over-fishing a district will be that of multiplying the 

 numbers. 



The results at which we have arrived here are found in 

 nature. One of the most obvious effects of over-fishing a 

 district is that there results a great number of small-sized 

 individuals of the particular species affected. Looked at from a 

 general aspect we may express this result thus: The species 

 is subjected to risks of extinction and the counteracting effect 

 is a reactive production of a greater number of smaller indi- 

 viduals, so that extinction may be prevented by multiplying 

 the chances of a sufficient number reaching sexual maturity. 

 The want of this ready re-activity to changed surroundings 

 in mammals helps to render the whales and seals liable to 

 extinction at the hands of man. 



In the case of birds and quadrupeds these laws apply, as 

 already stated, only to the extremely limited extent to which 

 the attainment of sexual maturity and the cessation of growth 

 do not quite correspond in point of time. Hence protective 

 reduction in size of a bird or mammal can only take place 

 at an extremely slow rate. 



The amount of growth of a fish per annum may be expressed 

 as a certain proportion of the whole, and must form an ever- 

 decreasing geometrical series, so that the total amount of growth 

 is only limited in the same sense asl+| + i + ^, etc., is limited 



