228 Mr. E. Warren. 



The critical function 2ft 3ft 6 =0*087561 is negative, and so 

 the theoretical curve has a limited range. The calculated range was 

 71*313123 units, and the observed range 21 units ; thus they differed 

 very widely. The range on the positive side of the origin was 

 31*658658, and on the negative side 39*654465. As the frequency 

 curve is very symmetrical, Professor Pearson's generalised curve with 

 limited range and symmetry was taken, 



where y = 186*357143. a = 35*656561. 



m = 66*048343. . 



The distance of maximum ordinate from centroid vertical is 0*0596, 

 and this could not be indicated on the scale of diagram. Both this 

 and the normal curve are drawn over the curve of observation 

 (fig. 3). The generalised curve differs exceedingly little from the 

 normal one, the areal deviations in the two cases being 7*7 and 7*5 

 per cent, respectively. 



The flat top to the frequency curve made it at first seem prob- 

 able that the curve was really the resultant of two normal ones. 

 It was attempted to resolve it into its constituents by means of Pro- 

 fessor Pearson's equation of the ninth degree ('Phil. Trans.,' 

 vol. 185). There were three real roots to the equation; two gave 

 quite inappropriate solutions; the third gave a negative group of 

 sixty crabs (with standard deviation = 1*450), having its maximum 

 ordinate situated at 1*337 from the centroid, and a positive group of 

 1492 crabs (standard deviation = 3*012), with maximum ordinate at 

 0*0540. The selection of crabs so close to the mean would scarcely 

 seem to correspond to any natural phenomenon, and the resultant 

 curve, which was the difference of the two normal curves, fitted the 

 curve of observation but very little better than the normal or skew 

 curve in fig. 3, the areal deviation being 7*0 per cent. 



L. Antero-lateral. Here the range of the mean is somewhat larger 

 than on the right side, being about 1 units. The range of deviation 

 in the whole series is 720 823 thousandths. A frequency curve was 

 drawn (fig. 4) with groups 6 12, where the range was 724 819 

 thousandths, giving 24 units. 



Centroid = 14*046787. ^ = 9*127467. 



a = 3*021170. ^ = -1*885642. 



p* = 263-267646. 



ft = 0-004676. ft = 3*160072. 



r = 42*246651. Skewness = 0*031099. 



