90 THE QUANTITATIVE METHOD IN BIOLOGY 



which has been developed under the same social conditions as 

 a.^ This problem is solved by determining the position of a 

 with regard to the system of axes of a and by finding in 6 a leaf 

 ^ which has the same position with regard to the axial system 

 of h. 



The method is applicable as often as the system of axes is not 

 too complicate. 



EXAMPLE : We want to compare two or several specimens 

 of Quercus robur pedunculata with regard to the primordia 

 length of the leaf and number of leaves. The question is com- 

 paratively simple if we take young specimens ; for instance, in 

 their third year. The main stem A may be practically looked 

 upon as consisting of three segments (successive annual shoots) 

 A + 1 coinciding with the three years. Each segment ^4 + i is 

 divided into internodes A + 2. The leaves may be counted, for 

 instance, in the third A + i (terminal shoot of the main stem). 

 The lowest (first) leaf of this segment ( = the first leaf of the 

 third yearly shoot) may be taken for the measurement of 

 the primordium length^ The mentioned leaf being measured 

 and the leaves being counted in all the specimens, social 

 variation is eliminated and the figures are comparable, just 

 as if we had measured, for instance, the breadth of the third 

 cervical vertebra in a number of specimens of one species of 

 mammalia. 



The above method, applied on a series of species of one genus 

 (or on the indigenous trees and shrubs) would give very inter- 

 esting results ; many characteristic features, many unsus- 

 pected similarities and differences would be discovered. For 

 such a comparison of different species it would be, of course, 

 necessary to take a number of specimens ^ of each species, 

 because individual variation ought to be taken into account 

 (Part VL). 



§ 75.— RAMIFICATION OF THE UNIAXIAL SYSTEM. 

 COMPLICATED CASES {continued). INDIVIDUAL DE- 

 VELOPMENT. PRIMORDIA OF THE SUCCESSIVE 

 UNITS OF ONE SPECIMEN. PRIMORDIA OF CUTTINGS 

 AND GRAFTS. — Suppose we want to study the embryology 

 of the leaf of Quercus pedunculata. If we take at random a 

 certain number of leaves in successive stages of development 

 and compare them, the observed differences certainly depend for 

 a part on the social differences between the investigated leaves 

 (which are individuals) . If we want to obtain exact results, the 



1 In other words, the leaf j8 ought to be a social equivalent of a. 



^ In reality it would be preferable to measure the longest leaf of the terminal 

 shoot. (See Gradation, Part VIII.) 



^ Material (seedlings) of many species may be obtained at a rather low price 

 from any well-equipped free nursery. 



