320 Prof. W. F. R. Weld on. On certain [Nov. 16, 



3. The frontal breadth, from tip to tip of the anterior lateral teeth 

 (fig. 1, CD). 



4. The right antero-lateral margin, from the tip of the median 

 inter-orbital tooth to the tip of the postero-lateral tooth (fig. 1, AF). 



5. The right dentary margin, measured in a straight line from the 

 tip of the antero-lateral to the tip of the postero-lateral tooth (fig 1, 

 DF). 



6. The left antero~lateral margin, measured in the same way as the 

 right. 



7. The left dentary margin. 



8. The sternal breadth, measured between the articulations of the 

 great chelaa. 



9. The meropodite of the right chela, measured in a straight line 

 between the inner articulations. 



10. The carpopodite of the right chela, from the inner articulation, 

 in a straight line to the tip. 



11. The proximal portion of the same carpopodite, in a straight line 

 from the inner articulation to the tip of the inner spine, at the base 

 of the dactylopodite. 



The dimensions 2 11 were expressed in terms of the total length 

 of the carapace taken as 1000 ; and, in order to reduce the effect of 

 possible errors of measurement, the values so obtained were grouped 

 together in fours, the groups being so selected that no two individuals 

 in any one of them differed by more than 0'004 of the carapace length. 



As an example of the way in which the values thus obtained were 

 distributed, the measurements of the right antero-lateral margin in 

 Naples and in Plymouth may be examined. The results of these 

 measurements are shown in Tables I and II. The frequency with 

 which every observed magnitude of this portion of the carapace 

 occurred in the Naples specimens is given in the second column of 

 Table I. The arithmetic mean of all these values is 752'22 thousandths 

 of the carapace length ; and the observations will be seen to cluster 

 with a fair degree of symmetry around this value, the symmetry of 

 distribution being, perhaps, more readily seen by the eye in the 

 diagram, fig. 2. The total number of individuals in the sample was 

 999, and of these 513 had the antero-posterior margin greater than 

 the average size, 486 having this portion of the carapace below the 

 average. The arithmetic mean of all the deviations from the average, 

 or "mean error" of distribution, was found to be 8'71 units; and 

 the modulus is therefore 8'71 x 1'77 = 15'42 units. A probability 

 curve, with modulus = 15*42 units, has been drawn by a dotted line 

 in fig. 2 ; and the close agreement between this curve and the observed 

 curve of distribution, which is indicated by a thick line, is very 

 striking. In order to make a more accurate comparison possible, the 

 number of individuals corresponding to each observed magnitude, on 



