2 74 PATTERNS AND PROBLEMS OF DEVELOPMENT 



system with reference to which axiate pattern develops. The question 

 whether and how specific differences can arise at different levels of a gradi- 

 ent is considered in another connection (p. 297) ; but, assuming for the 

 moment that this is possible, the conception of a gradient system as a 

 physiological co-ordinate system requires some further consideration, A 

 radial gradient system, such as that of many buds, results in a radial de- 

 velopmental pattern which becomes polar in consequence of differential 

 growth (p. 16); and a longitudinal system, like that of a Corymorpha 

 piece, results in a longitudinal developmental pattern, within which par- 

 ticular organs or parts arise at particular levels and where scale of organi- 

 zation can be increased or decreased by altering height and length of the 

 gradient (pp. 38, 344-57). But a question at once arises: Can two or 

 more gradients or gradient systems in two or more different directions in 

 the same protoplasm constitute a co-ordinate system which specifically 

 determines each region? In other words, can such a system determine the 

 developmental pattern of organisms with ventrodorsality or dorsiventral- 

 ity and often asymmetry? If the two or more gradients are of the same 

 kind and intensity, the chief axis of the pattern determined will be in the 

 direction of the resultant of the two. In the accompanying diagram (Fig. 

 107, A) anterior, posterior, dorsal, and ventral are indicated hy A,P, D, 

 and V. The anteroposterior gradient is indicated by the numerals 4-1 

 above; the ventrodorsal gradient, by the numerals on the right. The nu- 

 merals of the different areas are the sums of those indicating respective 

 levels of the two gradients; for the sake of simplicity the two gradients 

 are assumed to be additive in effect. The diagram shows that the chief 

 pattern differences are in the direction of the heavy lines oblique to both 

 gradients. The broken obUque lines indicate directions along which pat- 

 tern is the same. This is not the sort of pattern usually found in organisms 

 with a longitudinal and ventrodorsal axis. 



In Figure 107, B, the anteroposterior gradient is assumed to be opera- 

 tive and to have induced some degree of specific differences, a-d, at dif- 

 ferent levels before the ventrodorsal gradient becomes markedly effec- 

 tive, its effectiveness being assumed to increase gradually. In this case 

 each area is in different physiological condition and is defined by its rela- 

 tion to the two gradients, and the pattern has an anteroposterior and 

 ventrodorsal axis. If the ventrodorsal gradient is primarily quantitative, 

 its effect on the specifically different regions a-d may differ in character 

 because of their differences and may determine further alteration. Fig- 

 ure 107, B, serves merely to suggest in a general wav how a developmen- 



