62 THE QUANTITATIVE METHOD IN BIOLOGY 



contented myself with a mere estimation of the successive values 

 of the primordia. This method was applicable because it was 

 possible to bring side by side into a series and to compare a 

 number of specimens (florets of Centaurea cyanus) in various 

 states of development. But in order to obtain exact results 

 measurement is, of course, indispensable. 



An important question is to determine at which moment 

 the measurements ought to be made. Two general methods 

 (followed in embryology) may be adopted: 



(i) We may divide the time (hours, days, etc.) between the 

 beginning and the end of the development into a certain 

 number of intervals, measuring the properties at the end of 

 each interval. This method is applicable in certain cases ; for 

 instance, for the development of a bird or a fish within the eg^, 

 all the eggs developing under the same conditions. But this is 

 rather exceptional. The rapidity of development often varies 

 considerably according to external influences (temperature, 

 etc.). Therefore two embryos of the same age may be in a very 

 different state of development. It is, moreover, often impossible 

 to know the exact age of an embryo. 



(2) According to the second method, one property is taken as 

 a standard or leading property, the development of the others 

 being investigated in comparison with the standard. The 

 choice of a leading property is, of course, arbitrary, and depends 

 in each peculiar case on the investigated subject. In the 

 development of a fish, a leaf, a petal, etc., the total length of 

 the object is ordinarily a convenient leading property. 



I have adopted the method of the leading property in the 

 investigation of gradation along the stem of grasses and acrocar- 

 pic mosses (Part VIII.). (Compare § 114, Fig. 23.) See § 133. 



§ 50.— VARIATION IN EMBRYOLOGY.— Many embry- 

 ologists believe that variation does not exist or hardly exists in 

 the early period of development of higher animals and plants. 

 Conclusions drawn from the study of one or two specimens are 

 regarded as being applicable to the species and also (according 

 to the Haeckelian principles) to a whole genus and even to a 

 family or a class. For instance, a paper in which two embryos 

 of a tortoise are described is called a Memoir on the Embryology 

 of the ChelonidcB., etc. 



We know, on the other hand, that adult specimens are 

 variable in their internal anatomy just as in their external 

 properties. I have investigated by measurement thirty-eight 

 properties in about ninety species and twenty-five so-called 

 varieties of the genera Carabus and Calosoma.^ I have found a 



^ I have carried out about 250,000 measurements (September 1907 to July 

 1914)- 



