200 THE QUANTITATIVE METHOD IN BIOLOGY 



Each of the above segments consists in its turn of a number 

 of units of the third order called internodes. All the segments 

 or units (of the second and the third order) follow each other m 

 the direction of one straight line, which is the axis. The whole 

 system (specimen) is therefore a uniaxial system. 



The axis is a Hne of ordonnance. It is characterized by three 

 facts : it is a Une of : (i) segmentation ; (2) differentiation ; 

 (3) gradation. 



With reference to the latter point I measured the primordmm 

 (simple property) length of the successive internodes from the 

 base to the summit (the terminal spikelet being excluded) of 

 two flowering stems taken at random. ^ 



The figures are given in the f olloving Table : 



Length of the successive internodes of two flowering stems of Poa tyivialis. 

 The terminal spikelet is excluded. The internodes are numbered (I., 

 II. . . .) from the base to the summit. The limit between the stem 

 properly so called and the inflorescence is indicated for each stem by ] [. 

 Length in mm. 



Internodes 

 Length ist stem 

 Length 2nd stem 

 Internodes 

 Length ist stem 

 Length 2nd stem 

 Internodes 

 Length ist stem 

 Length 2nd stem 



Each of the above series of figures represents an individual 

 gradation curve (specimen curve) . By means of the figures of 

 each series (I take the first stem as example) .we may draw the 

 curve (Fig. 26), in which the axis (stem) is represented by a 

 horizontal Une, the length of the successive internodes being 

 represented by equidistant vertical ordinates. Such a curve is 

 merely a graphic representation of facts without any calculation. 



It is seen that in both stems the value of the primordium 

 under consideration increases from the base ^ till a maximum 

 is reached and further diminishes towards the summit. The 

 curve has thus an ascending-descending form. The slight 

 irregularities which occur at several places (for instance, 2nd 

 stem, internode IV.) are brought about by accidental causes 

 (chance). 3 



1 It happened that the total number of internodes was the same in both — 

 Adz. 21. This is not always the case. 



^ The value y of any ordinate depends on the distance comprised between 

 its base and the origin /. In other words y =fx. 



' A number of similar curves have been described by PERCY GROOM 

 in his interesting paper on " Longitudinal Symmetry in Phanerogamia," 

 Phil. Trans. Roy. Soc, London, ser. B., vol. cc. (1908), pp. 57-115, with numer- 

 ous figures. 



