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BIOLOGICAL LECTURES. 



It has been urged by some naturalists that the quantitative 

 study of animals will take away that peculiar charm which 

 attaches to biological study. This peculiar charm, as I under- 

 stand it, is due to the contact with out-of-doors, into which the 

 biologist is brought, and to the fact that the phenomena which 

 he studies of growth, reproduction, variation, inheritance, and 

 differentiation of form and activities, of structure and habits, 

 form an important part of human experience. Now the stu- 

 dent of variation also is concerned with these same phenomena, 

 only he uses a different method in his study of them. More- 

 over, the necessity of collecting large numbers of individuals 

 for study will be especially apt to take the student to the field. 

 After all, it is the search for truth, particularly a truth which 

 seems worth while, which inspires us, and the quantitative 

 method gives us a new tool in this search. 



There seems to be an impression that all this quantitative 

 work is very difficult. But this is not at all the case. Many 

 important pieces of work require only abundant material and 

 the ability to count and record. Thus, by counting the ray 

 flowers of the field daisy, Ludwig discovered that in the distri- 

 bution of their frequencies they exhibit several " modes " occur- 

 ring in a mathematical series — the series of Fibonicci. By 

 counting the grooves in scallop shells from two Long Island 

 localities, I have found a significant difference in the variability 

 of the upper and lower valves, and also a difference in the aver- 

 age number of grooves from the two localities. With the aid of 

 a hand lens only, a series of studies has been made on the vari- 

 ability of the rostral teeth of prawns from different countries and 

 from the same country, but subjected to various conditions. Of 

 course, with the aid of a millimeter scale, dividers, planimeter, 

 map measurer, color top, balances, and other apparatus, one 

 can go farther. As to the number of individuals required, at 

 least from two hundred to five hundred should be employed 

 when possible. 



Not only the qualities of the form-unit, but the causes which 

 have determined those qualities are to be investigated quanti- 

 tatively. Among these, selection, the direct action of environ- 

 ment, and internal tendencies to change are reckoned the most 



