48 THE ROYAL SOCIETY OF CANADA 



at the same rate. The difference in appearance between the winter 

 and summer zones is brought about by a difference of growth within 

 the scale, whereby in the slow period of growth new rings, or circuli 

 as they are called, are formed more rapidly than the scale increases 

 in diameter, so that the circuli are crowded together. That is, the 

 very use of the scales in age-determination depends upon differential 

 growth within the scale. 



The importance of recognizing and allowing for this lack ol 

 correspondence in the growth of the scale and the growth of the 

 fish will be evident from the following example. A flat-fish (Hip- 

 poglossoides platessoides) 132 m.m. long from Passamaquoddy Bay, 

 captured on November 15th was completing its second year's growth. 

 Calculation of its size at the end of the first year by the method 

 described gave a length of 22 m.m. when a large scale from the side of 

 the tail was used, and one of 12 m.m. when a small scale from near 

 the posterior fin was used. Both of these values are much too small, 

 foi; the scales do not appear until the fish is about 30 m.m. long. 

 By using the method of calculation which will be described a value of 

 44 m.m. was obtained, whether the scale used were large or small. 



This method of calculation, which takes into account the dif- 

 ferential growth of the scale and the fish, is as follows. The part of 

 the scale which shows the summer and winter zones most clearly is 

 the anterior part, which is covered by the scales in front. The 

 dimension used in length calculations is from the focus, or centre of 

 origin, to the anterior tip, and its average value in scales of a certain 

 kind {e.g. the scales from the side of the tail) is found for fishes of 

 different sizes. As an example in the case of the flat-fish II. plates- 

 soides five individuals of each of the following lengths were taken— 

 5, 10, 15, 20, 25, 30, 35, 40, 45 and 50 cm., and for each individual 

 five 'tail' scales were taken and the average value of the dimension 

 found. Then the average value of the dimension for the five individ- 

 uals of each size group was determined and these values plotted 

 against the lengths of the fishes as shown by the upper series of dots 

 in figure 1. The curved line drawn as nearly as possible through 

 these dots represents the probable average relation of the dimension 

 to the length of the fish. This curve originates in the base line at a 

 length of the fish of about 3 cm. This curve may be used for the 

 length-calculations. If from a certain fish a scale be selected with 

 the distance from the focus to the anterior end equal to the average 

 value of that dimension for the size to which the fish belongs, it will 

 be comparatively easy to determine the yearly growth by measuring 

 the successive zones and finding by reference to the curve the amount 

 of the length of the fish to which each zone corresponds. For example. 



