METHODS OF INVESTIGATION. 



29 



The measurements thus obtained have been used for calculating the 

 size of the fish at the time when the growth of each winter-band was com- 

 pleted. The calculations have been made by taking the measurement from 

 the centre to the anterior edge of the scale as equivalent to the total length 

 of the fish, and from this the value for each winter-band can be arrived at 

 by a proportionate calculation. The calculation is made by means of an 

 apparatus constructed by Mr. Lea and myself, by which the proportionate 

 values of each winter measurement are graphically shown, and by its use 

 we have been able to accomplish the 

 work rapidly and accurately. The 

 apparatus and the method of using it 

 have been fully described by Mr. Lea 

 in the paper mentioned above. 



In this way I have calculated the 

 lengths of a number of fish on the com- 

 pletion of the first, second, third, &c., 

 winter - bands, and the results thus 

 obtained are shown in the analytical 

 tables of the fish examined by this 

 method. 



If one can obtain satisfactory results 

 by the adoption of this method the 

 advantages are obvious. If, for example, 

 I obtain a collection of fifty fish equally 

 divided amongst five different year- 

 classes, it is evident that by ordinary 

 methods I have only ten examples on 

 which to base my calculations for the 

 average length of each class. On the 

 other hand, by adopting this other 

 method I am able to make far more 

 observations. If, therefore, this method 



is sound a relatively smaller number of examples would be sufficient to 

 enable one to draw up an equally serviceable growth-curve, and we should 

 be able to avoid having to collect such a large number of specimens, and 

 so avoid the enormous amount of time and labour involved in the collection, 

 examination, and analysis of one's material. 



I am quite aware that one may adduce reasons for believing that the 

 length of the scale (the anterior or differentiated portion) may not grow in 

 a manner absolutely proportionate to the total length of the fish. Amongst 

 other things, I have found that in the case of trout a slight alteration occurs 

 with age in the relative size of the head and the tail in comparison with 



FIG. 26. 



