90 



DEPARTMENT OF THE NATAL SERVICE 



6 GEORGE V, A. 1916 



would have been a valuable check upon the curves for different ages as determined 

 by assuming the growth of the scales to be proportional to that of the fish, which are 

 described beWw. The curves for the three-year-old fish (fig. 3) naturally showed little 

 difference from the length-frequency curves for all of the sex, the same humps appear- 

 ing distinctly in each case. 



Whether the growth of the scale is proportional to that of the fish could not be 

 definitely determined owing to the impossibility of comparison of curves obtained 

 upon this assumption with ordinary length-frequency curves for different ages. Th© 

 assumption was made, however, and certain deductions were drawn as to the rate of 

 growth. 



A scale was placed under a low power of the microscope, and by means of a camera 

 lucida a line was drawn, representing the long axis of the scale from the centre to the 

 anterior extremity, and the positions of the lines of growth were marked upon this 

 line (fig. 4). Another line, representing the short axis from the centre to one side 

 was similarly drawn and marked off, the two lines being so placed that they formed a 



Fig. 3. — Length-frequency curves for 38 male and 42^ female hake all three years old. 

 Curve for females a continuous line, cvuve for males interrupted line. The posi- 

 tions of the means are indicated by dotted lines. 



wide angle, the ends representing the outer ends of the axes coinciding. Between 

 these lines there was then drawn from the angular point a third line representing the 

 length of the fish, the scale being 2 mm. to 1 cm. Straight lines were now drawn from 

 the ends of the two lines representing the axes to the end of the third line, and lines 

 were drawn parallel to these from the positions of the lines of growth to meet the 

 line representing the fish. In this way the length of the fish at the end of each year 

 of its life was determined graphically. Unfortunately it was found that the two axes 

 gave different results, and there was no fixed relationship between them. For this 

 reason the construction was always made for both axes, as described, and the average 

 of the two results was taken. In several cases the construction was made for more 

 than one scale of the same fish. The results obtained in this way differed just as 

 irregularly as did those given by two axes of the same scale, and again the average 

 was taken. 



Fifty females ,and forty-five males (all the males of which scales had been taken, 

 except a few in which the number of lines of growth was doubtful) were examined in 

 this way, and length-frequency curves were drawn for the different ages of each sex 

 (Figs 5 and 6) from the lengths calculated as above, upon the assumption that the 

 growth of the scales is proportional to that of the fish. Two of the lengths calculated 

 for males at the end of the first year, one at the end of the second year, and two at 



