30 THE MEASUREMENT OF VARIATION. 



High blossoms, 01 23456789 10 

 Frequency obsd. 325 83 66 51 36 36 18 7611 

 Theory, 303.2 106.1 70.0 49.3 35.2 24.9 17.1 11.0 6.3 2.8 .5 



J. H. Pledge * observed the following frequencies in 

 the numbers of petals in Ranunculus repens : 



Number of petals, 4 5 6 7 8 9 10 11 12 13 

 Frequency, 8 706 145 72 38 15 7 7 1 1 



Again E. T. Browne f found the following variations 

 in the number of tentaculocysts in the ephyra and adult 

 forms of the medusa Aurelia aurita : 



Tentaculocysts, 45678 9 10 11 12 13 14 15 

 Percentage in 



1136 ephyrse, .09 .5 3.0 79.1 6.7 5.4 3.1 1.4 .2 .09 

 Percentage in 3000 



adult Aurelia, .1 .1.74.178.9 6.3 4.8 3.0 1.4 .4 .1 .1 



In each case the normal eight tentaculocyst form com- 

 prised nearly four-fifths of the whole, but the great 

 majority of the abnormal forms possessed more than 

 eight tentaculocysts, only 3.6 to 5.0 per cent, of them 

 having less. 



Now the distribution of frequencies in these and 

 somewhat similar asymmetric series obviously occurs ac- 

 cording to some orderly plan, but can a mathematical 

 expression be obtained to represent them? This had 

 been found impossible till within the last few years, 

 when Professor Pearson $ took up the subject, and 

 showed that such series, if composed of homogeneous 

 material, could often be fitted most exactly with curves 

 calculated in accordance with a single generalised 



*Nat. Science, vol. xii. p. 179, 1898. 



fQ. J. Microsc. Sci., vol. xxxvii. p. 245, 1895, and Biometrika, 

 I. p. 90, 1901. 

 JPhil. Trans. 1895, A. p. 343, 



