228 DISCOVERY REPORTS 



monthly period is seen to consist of a number of groups distinguished by definite modal 

 lengths. The modal length of each separate curve of error, indicated in the figures by the 

 perpendicular dropped from the modal point of each curve, has then been plotted on the 

 circular graphs, Figs. 9 and 12. In these graphs the circles represent carapace lengths, 

 the origin being at the common centre. The circles are placed 2 mm. apart and so 

 correspond with the frequency classes of the curves of Figs. 8 and 11. The six equally 

 spaced radii represent the six bi-monthly periods of the year, and along each radius have 

 been plotted the modal lengths of each separate curve of error present in the corre- 

 sponding bi-monthly graph. The values of these modal lengths are shown by crosses 

 along the radii. Where a modal length is based upon less than 10 per cent of the total 

 specimens for any period, its position is marked by a smaller cross than that employed 

 for modal lengths based upon more than 10 per cent of the total specimens for the 

 period. When all the modal lengths are thus plotted it is found that a smooth curve of 

 ever-increasing radius can be drawn through the majority of the points. This curve is 

 not a true helix, for the increase in radius is not constant ; but it is a reasonably smooth 

 curve passing through practically all the points without retrogression and may be 

 termed subhelical. This curve illustrates the growth throughout the life of an average 

 individual. 



The curves thus obtained on the circular graph can be readily transferred to the usual 

 rectangular form of graph as in Figs. 10 and 13. Here the bi-monthly periods are shown 

 along one axis, carapace lengths along the other. The points on the circular graph are 

 then plotted in the order in which they are met as one travels along the subhelical curve 

 from the origin. In Figs. 10 and 13 no line has been drawn through these points, but 

 they lie along a curve showing rapid growth in the early part of life, gradually slowing 

 down until growth almost ceases. This is, of course, a reflection of the changing rate of 

 increase of the radius of the subhelical curve in the circular graph. 



Considering now the graphs for female M. subrugosa, the smallest specimens are seen 

 to have been taken in the period April-May, the curve of error of this group giving a 

 modal value of 6-5 mm. The next point occurs in August-September at lo-o mm. ; but 

 this young group was not sampled in October-November. The point in December- 

 January at almost 11-5 mm. is based on less than 10 per cent of the catch for that period, 

 but lies easily on the curve leading to the point at slightly more than 15-0 mm. in 

 April-May. The female M. subrugosa has now completed the first year of post-larval life 

 and the carapace has increased in length from 6-5 to 15-0 mm. The female is now 

 sexually mature and can be found carrying eggs at carapace lengths from 12-0 mm. The 

 onset of sexual maturity probably accounts for the slowing down of the growth rate to a 

 steady increment of about 4-0 mm. each year which now takes place. In the circular 

 graph a slight regression is seen in the third year, from 21-3 mm. in October-November 

 to 21 -o mm. in December-January. Apart from this rather trifling aberration, almost 

 four years of growth can be traced with reasonable accuracy by this method. 



The rectangular graph showing growth (Fig. 10) gives a picture of a post-larval life 

 of some six years. During this time the carapace length of the female M. subrugosa 



