Rate of Growth in Gobi us minutus. 223 



pressed by a constant formula. There are always exceptional 

 cases which seem to disprove the most carefully constructed 

 theories in this connexion. But when one considers the 

 changing conditions of the food-supply, o£ temperature, of 

 fitness for survival of individuals, and of specific variation, 

 such exceptions must be inevitable. A 40 mm. form was 

 captured at St. Andrews towards the end of April. Supposing 

 this was one of the group which reached 20 mm. in the pre- 

 ceding September, a growth of 20 mm. would have occurred 

 during the seven intervening months. This only allows an 

 increase of approximately 3 mm. per month, during the 

 months of late autumn, winter, and early spring. In a case 

 of this nature the rate of growth per month works out too 

 low in the estimation of the writer, and the age of the fish 

 has been calculated as if it had been hatched at the end oi 

 June or early in July, in other words, a month later than the 

 typical period. Thus the age of this 40 mm. specimen 

 caught in April is given as 10 months. In each case the 

 " Calculated age" has been arrived at by such arguments as 

 the above. 



The figures included in the four statistical tables were 

 reduced to a graphical form. The horizontal line was divided 

 into equal spaces, each representing a month from May 

 onwards *. The vertical line represents the average length 

 of the fish in mm. The dark line drawn parallel to the basal 

 line, and 1*5 mm. distant, marks the average length at which 

 gobies are hatched from the egg. The points on the graph 

 indicate the average length of lish actually caught on a given 

 date. Thus, two gobies averaging 9'0 mm. were caught at 

 St. Andrews on 13/7/88 ; taking Graph L, St. Andrews, and 

 following the horizontal line nearly to the point representing 

 the middle of the first July after hatching, then turning in a 

 vertical direction till the 9 mm. horizon is reached, the point 

 representing the above catch is encountered. An element of 

 inaccuracy is introduced here again by the fact that no account 

 is taken of the year in which the fishes were collected. The 

 dotted lines joining the points on the graph represent the 

 author's views with regard to the rate of growth. For 

 instance, in Graph I., St. Andrews, one of these lines joins 

 a point on the 5*5 mm. line above the first third of the space 

 representing June to a point on the 17*2 mm. line above the 

 far end of the space representing July. This implies that a 



* The spaces should have been proportional to the days of the month 

 which they represent ; but for practical purposes the slight error intro- 

 duced may be neglected. 



