THE MEASUREMENT OF VARIATION. 21 



for woman's; 2.92 per cent, for the span of arms of 

 both man and woman; but no less than 6.89 per cent, 

 for man's weight, and 8.89 per cent, for woman's. That 

 is to say, weight is more than twice as variable as the 

 other two characteristics. In most of Weldon's shrimp 

 and crab measurements the amount of variability was 

 considerably smaller, but this was partly due to the fact 

 that the element of size was largely excluded by first 

 of all calculating all measurements as thousandths of 

 the body and carapace lengths respectively. In 1000 

 shrimps from Plymouth, the total carapace length had 

 a relative probable error of only 1.82 per cent., the 

 post-spinous carapace length one of 1.97 per cent., the 

 sixth abdominal tergum one of 1.93 per cent., and the 

 telson one of 2.36 per cent. In 999 crabs obtained 

 from Naples, the value was only 1.07 per cent, for the 

 total breadth of carapace, and from 1 to 2 per cent, 

 for several of the other measurements made, but in the 

 carpopodite of the right chela it rose to 3.63 per cent., 

 and in the proximal portion of the chela to no less than 

 5.77 per cent. These last were, however, quite ex- 

 ceptionally large degrees of variation. Still, in the sea- 

 urchin larvae measured by the author, the variability 

 was found to be greater than in any of these instances 

 recorded in the higher animals, it being 6.1 per cent, 

 for the body length, 9.4 per cent, for the oral arm 

 length, and 11.3 per cent, for the anal arm length. 



We have seen that the degree of correspondence of 

 the variations in any characteristic with the law of 

 error can be determined by plotting out the results in 

 the form of a curve, but this is clearly a somewhat 

 laborious process. It is much simpler and more con- 



