1916] Introduction xxi 



water filtered during each luud may be eoinputed and eoniparetl with 

 each other. This, of course, is much more accurate and makes a more 

 thoroughgoing statistical treatment possible. 



Preliminary and supplementary to the employment of these quan- 

 titative methods, the data are examined in a more cursory manner for 

 the purpose of ascertaining, in a general way, the degree of corre- 

 spondence between the biological and hydrographic data. For example, 

 the center of population of Sagitta bipunctata undergoes a seasonal 

 oscillation from its maximum depth in winter to its minimum depth 

 in summer. In attempting to find a corresponding oscillation in one 

 of the environmental elements, the temperature range pertaining to 

 this center of population was discovered to be confined to a larger 

 and deeper depth interval in winter than in .summer. Combining these 

 two facts a single descriptive statement is obtained, namely, that the 

 vertical o.scillation of the center of population is apparently correlated 

 with a corresponding oscillation of the temperature distribution, or 

 "thermocline. " In order to test the extent and validity of this 

 apparent correlation recourse is had to the more rigorous methods just 

 described. 



A more detailed consideration of these methods would require more 

 space than is available in this paper. It would involve discussing the 

 relation between frequency and abundance, how the frequency may 

 be standardized when the average volume of water filtered differs, and 

 how the unit volume of water filtered is measured. It would neces- 

 sitate considering the use of geometric means, coefficients of association, 

 coefficients of preference, methods of eliminating the effects of one 

 variable upon the others, and methods of dealing with accidental and 

 systematic errors. It would require an explanation of why the usual 

 methods of linear and multiple correlation, and the probable error 

 method cannot be legitimately applied to distribution problems of the 

 type herein considered ; and it would require an explanation of the 

 methods employed in their places. Suffice it to say, therefore, that 

 other papers are being prepared in which all of these matters will 

 be diseu-ssed in detail. It is hoped, however, that this brief account 

 will give some idea of the methods employed. 



