1895.] into the Measurable Characteristics of Plants, tyc. 363 



Table I. Mean Frontal Breadth (F) expressed in thousandths of the 

 Carapace-length, corresponding to various Carapace-lengths (C), 

 together with the Number of Individuals on which each Deter- 

 mination is based. 



[Note. The carapace-length given in the table is the mean of all lengths 

 included in each group. For example, the entry 7'1 includes all crabs measured 

 in which the carapace-length was between 7'00 mm. and 7'19 mm., and so on.] 



vations no satisfactory demonstration of the law of variation at any 

 given moment of growth could be obtained. Nevertheless it was 

 necessary, before proceeding further, to ascertain with some certainty 

 what the law of variation through the whole series really was. The 

 belief in which the work was undertaken was, that the law of varia- 

 tion would be found throughout to be that of the ordinary probability 

 equation ; and this belief was tested in the following way : In each 

 of the thirty-five groups, the arithmetic mean of the frontal breadths, 

 and the mean of all the deviations from it, were determined ; and 

 from the " mean error " found in this way the modulus of the 

 probability function was calculated. Then, -by calling the mean of 

 each group zero, and expressing the deviations from the mean in 

 terms of the modulus, a number of curves were obtained, in each of 

 which the modulus was unity and the mean zero ; a similar curve of 

 adults was constructed, and the corresponding ordinates of all the 

 thirty-six curves so obtained were added together, It is evident that, 

 if the chance function really expresses the law of variation throughout 

 the series, then the curve resulting from the treatment described will 

 be a symmetrical probability carve of unit modulus. The actual 

 VOL. LVII. 2 D 



