102 THE QUANTITATIVE METHOD IN BIOLOGY 



this continuous gradation. In the conical hair represented in 

 Fig. 5 (p. 87), for instance, the gradation of the primordium 

 breadth of the cells is continuous along the axis. 



When, on the contrary, a sudden change is observed in the 

 value of ^ at a certain level of the axis, gradation is discon- 

 tinuous and produces differentiation. 



EXAMPLE : An antenna of Carahus is (with regard to the 

 exoskeleton (=cuticula)) a uniaxial system divided into eleven 

 segments (articles). ^ The gradation of the primordium length 

 of the segments may be described (in the majority of the species) 

 in the following way : — 

 Joint I : long. 

 „ 2 : short. 

 „ 3 : long. 

 „ 4 : short. 

 „ 5-1 1 : length decreasing gradually from 5 to 11. 



Here joint 2 is differentiated from i and 3. Between 3 and 

 4 the differentiation is very distinct in certain species, less 

 distinct in others. From 5 to 11 the gradation is almost always 

 continuous. 



Between typical continuous gradation and typical discon- 

 tinuous gradation {differentiation) all possible transitions 

 exist. 



In a chess-board system continuous gradation (Fig. 13, 2), 

 typical differentiation and aU possible transitions between both 

 may be observed in the direction of one or both axes and in 

 various primordia. 



EXAMPLE: The epidermis of a young leaf of Allium 

 porrum is divided in the direction EW into a number of seg- 

 ments, each of which consists of one longitudinal row of cells, 

 in the same way as the epidermis of an onion scale (Fig. 9, 

 p. 96). In each cell we may distinguish an extremity S 

 (proximal) and an extremity N (distal) ; a latent cause of 

 gradation according to the axis NS exists in each ceU. At a 

 given moment of the development each cell (unit x + 2) is 

 divided into a northern cell b and a southern cell a, and now 

 gradation finds its visible expression, the A^-ceU b being much 

 shorter than the 5-cell a. Since the difference in length 

 between a and b is very distinct, we may say that gradation 

 results here in differentiation. 



Later on a second difference between a and b becomes appf J- 

 ent (Fig. 14) : a develops into an ordinary epidermal qell, 

 whereas b is divided (in the direction EW) into two cells 

 which form a stomate. In this way the curious differentiaition 

 of the units (longitudinal rows) x+x into alternative sto/matic 



1 In reality, the segments are twelve in number, the first segment being very 

 small and concealed. 



