CONTRIBUTIONS FROM THE ZOOLOGICAL LABORATORY OF THE 



MUSEUM OF COMPARATIVE ZOOLOGY AT HARVARD 



COLLEGE, E. L. MARK, DIRECTOR, NO. LXXIX. 



A MEASURE OF VARIABILITY, AND THE RELATION 



OF INDIVIDUAL VARIATIONS TO SPECIFIC 



DIFFERENCES. 



By Edwin Tenney Brewster. 



Presented by E. L. Mark, April 14, 1897. 



Problem. 



This paper, prepared under the supervision of Dr. C. B. Davenport, 

 deals with an inquiry into the relation between those small variations 

 which distinguish individuals of the same group, and those larger differ- 

 ences which separate species and genera. 



For the prosecution of such an inquiry, it is, first of all, necessary to 

 devise a method of measuring variability. Quetelet ('46), Stieda ('82), 

 Galton ('91), and Weldon ('93) have shown that variations in organisms 

 follow the well known laws of the distribution of error. Thus the ordi- 

 nary methods of treating problems in error of observation may be made 

 to furnish a measure of variability ; it is upon these methods that the 

 methods of this paper are based. 



Method. 



Any measurable quality of an object has a value, which is expressible 

 by a number. A series of such numbers, expressing the varyino; value 

 of a quality throughout a group of similar objects, will have a mean, 

 about which the quantities are arranged in accordance with the law of 

 distribution of error. Such a series is, for the present purpose, essen- 

 tially like a series of slightly erroneous observations of a single quantity 

 distributed about the true value. What, therefore, would be the proba- 

 ble error in the latter case, is a measure of variability in the former. 



Suppose such a series of numbers obtained by measuring some single 

 quality in each individual of a natural group of organisms. Let there be 



