268 BIOLOGICAL LECTURES. 



nature ; not indeed the species of the systematist, but rather 

 those homogeneous lots of individuals taken from one locality 

 to which Duncker has given the convenient name "form-units." 

 The quantitative method of studying the form-unit consists in 

 counting certain numerically repeated organs, or of measuring 

 one or more organs, on each of many individuals. The quan- 

 tities resulting from these measurements are then "seriated" 

 or arranged in classes according to size. More quantities will 

 fall in certain of these classes usually the middle classes 

 than in the others. The distribution of "frequencies of occur- 

 rence" in the several classes will give those characters of the 

 form-unit for which we are seeking its rigidity or plasticity, 

 its stability or instability, its independence of or subjection to 

 selection, and its unity or its tendency to break up into several 

 forma. From a comparison of measurements of two or more 

 organs of the same individuals we may learn additional facts 

 concerning the form-unit ; such as the degree of correlation 

 existing between its different parts, from which we may infer 

 directly the morphogenetic kinship of the different organs, 

 and, more indirectly, get light on homologies. The quanti- 

 tative study of the form-unit thus bears on many biological 

 topics. 



The possibility of getting such biological data from statistics 

 of organisms depends upon the fact that biological statistics 

 more particularly the distributions of "frequencies" follow 

 definite laws capable of mathematical expression and analysis. 

 The mathematical analysis necessary to deduce the biological 

 results is not very difficult, but is quite within the range of 

 any one who has studied trigonometry and logarithms. 1 



The objection has been raised that the quantitative method 

 of investigating the form-unit is limited to organs which can 

 be counted or measured with a millimeter scale. It is, how- 

 ever, applicable to the study of all quantities which can be 



1 For an account of the methods of dealing with biological statistics, see a 

 paper by Dr. Georg Duncker, on " Variations-Statistik," in Roux's Arch. f. Ent- 

 wickelungsmechanik, 1899, sold separately by W. Engelmann, Leipzig; and my 

 little book, Statistical Methods with Special Reference to Biological Variation, 

 published by John Wiley & Sons, New York, which contains also all the tables 

 necessary for the mathematical analysis of frequency distribution. 



