362 Report of the Committee for conducting Inquiries [Feb. 28, 



the field of a microscope, and by means of graduations on the head 

 of the screw the observations were recorded to the nearest hundredth 

 of a millimetre. It is believed that the probable error of any obser- 

 vation is not much more than one hundredth of a millimetre. In 

 order to minimise the effect of errors of observation, the results, after 

 being expressed as fractions of the carapace-length, were sorted into 

 groups, such that the measures in each group did not differ by more 

 than 0'004 of the carapace -length, and all measures in the same group 

 were treated as identical. The unit employed in tabulating the 

 results was therefore 0'004 of the carapace-length; but in what 

 follows the results are expressed, for the greater convenience of the 

 reader, in thousandths of the carapace-length. It will be noticed 

 that the principal effect of this alteration upon the results is to 

 dimmish their apparent regularity an aberration of one unit of 

 measurement appearing as four units in the tables below. 



1. Variation in Frontal Breadth. 



An initial difficulty in determining the error of distribution of 

 frontal breadths about their mean in young crabs, arises from the 

 great rapidity with which the mean itself changes during growth. 

 The menn frontal breadth in the smallest specimens was found to be 

 853*14 thousandths of the carapace-length, while at maturity it is 

 only 604*94 thousandths. The rate at which this change occurs can 

 be gathered from the following table of the crabs measured, and the 

 same result is graphically shown in fig. 2, 



From this table it appears that the mean frontal breadth changes 

 at such a rate that when the carapace-length has increased 02 mm., the 

 frontal breadth has almost always diminished by less than four thou- 

 sandths, that is to say, by less than one of the units of measurement 

 here employed. For the purpose of the present investigation the mean 

 was therefore considered stationary during every period of increase 

 in size of not more than 0*2 mm., and the young crabs were accord- 

 ingly sorted into groups, the individuals of each group differing bv 

 less than - 2 mm. in respect of their carapace -length. The distribu- 

 tion of frontal breadths about the mean was then examined in each 

 group separately. 



As the difference in size between the largest and the smallest of 

 the growing crabs was 7 mm., it follows that the material was divided 

 into thirty-five groups. This subdivision of the material had great 

 disadvantages, because, instead of a single group of over 7000 indi- 

 viduals, varying about the same mean, from which a fairly reliable 

 indication of the law governing frequency of deviation might have 

 been expected, the average number of individuals in any one of the 

 available groups was only 200 ; and from so small a number of obser- 



