of the Fishery Board for Scotland. 143 



spending dimensions — a law which was brought prominently forward by 

 Herbert Spencer in his " Principles of Biology " — a fish which has doubled 

 its length should have increased its weight eight times. This law is a 

 very convenient one in considering the rate of growth of fishes, all that 

 is required, if the law holds true throughout, being to determine the 

 relation between the weight and one of the dimensions at a particular 

 size and then calculate the ratio between that dimension and the weight 

 at different sizes. The truth of the law has not, however, been proved, 

 experimentally in the case of fishes, as far as I am aware, and it was 

 decided to actually measure and weigh a large number of fishes of 

 difTerent sizes, and to construct curves in order to bring out the relation 

 between the length and the weight at different sizes. In the Twentieth 

 Annual Report of the Fishery Board* I described the method of 

 presentation I had adopted, the absciss;e in the diagrams representing 

 length and the ordinates weight; and I pointed out that the curves 

 varied for different species, and that they did not everywhere agree with 

 the rule as to similarly-shaped bodies above referred to. 



Since then many more fishes and observations have been added to my 

 lists, and I propose to discuss some of the results now. 



In all cases, unless where otherwise stated, the observations have been 

 made at difierent times of the year, and on fish from different localities. 

 This method will give a better result as to the relations between length 

 for the species generally, although it is probable that the ratio varies 

 somewhat at different places and at certain times of the year — at all 

 events in fish which have reached adult size. This is referred to at 

 greater length below. 



In the observations made on this subject each fish was individually 

 measured in millimetres and then weighed in grammes, and the method 

 adopted in presenting the results was to collect the records of weight to 

 the nearest "5 centimetre, and take the mean of the lot. Thus the 

 number of observations under each "Scm. are often unequal in amount ; 

 but it was found, on testing the method, that this system gave practically 

 the same result as when the calculations were made for the observations 

 under each millimetre measurement — a very laborious process. 



The mean weight under a given "Scm. was then tabulated, as well as 

 the number of fishes at that size and the greatest and lowest weight 

 among them, and this information for the various fishes dealt with is 

 given in a series of tables appended (p. 205), while the average weight is 

 represented in the series of diagrams (Pis. VI, VII). In constructing these 

 curves the average weight of the fishes at a particular length was not 

 itself taken, the series of averages being arithmetically smoothed, by 

 taking the mean of the averages immediately before and after ; as a 

 rule only the one preceding and the one following was combined with the 

 average being smoothed, but in some cases where the number of 

 observations was small a number of the preceding and succeeding 

 averages were combined also and the mean taken. 



The fishes in which the relation between the length and weight at different 

 sizes were determined were the following : — Plaice, common dab, lemon 

 dab, long rough dab, witch, brill, cod, haddock, whiting, herring, sprat, 

 Norway pout, and partly also the turbot, little sole, gurnard, halibut, 

 flounder, armed bullhead, and Lumpenus. 



It will be seen from the tables and the curves of these fishes how very 

 greatly the weight for a given length differs in different species, and thus 

 how very different is the increment of growth for a given increase in the 

 length. Among the food-fishes examined by far the heaviest in proportion 



* Page 334, 1902. 



