42 POLARITY AND SYMMETRY; 



The direction of the plane of symmetry, however, may be 

 determined by the last two factors. According to Ancel and 

 Vintemberger, these factors cause a slight asymmetry in the 

 position of the cortex relative to the internal parts of the egg. 

 This would then direct the development of bilaterality. 



We have already said that the phenomena of polarity and 

 symmetry complicate the very simple picture of the egg drawn 

 in the previous chapter. They show that it would not be correct 

 to regard the egg as a completely homogeneous system. Polarity 

 and symmetry can only be explained on the assumption that 

 there are local differences in composition within the egg, and 

 a closer examination of the egg proves the truth of this as- 

 sumption. Some of its physical and chemical properties appear 

 to be unevenly distributed. As a rule, these properties have the 

 character of gradient systems. Therefore we shall now briefly 

 consider the meaning of this "gradient" concept. 



By "gradient- field'' is meant a spatial distribution of a 

 physical or chemical quantity, whereby the value of this quan- 

 tity gradually changes from point to point. The properties 

 concerned are always so-called "scalar" quantities, i.e. a 

 numerical value can be attributed to them (which might be 

 read on a scale), but no direction; e.g., temperature, pressure, 

 concentration of a substance, electrical potential, and the like. 

 In a gradient-field, we can distinguish planes of equal intensity. 

 At all points in such a plane the scalar quantity has the same 

 value. The rate of change of the quantity at any given point 

 in the field is called the gradient at that point. At each point 

 of the field, the gradient has one, and only one, definite value 

 and direction, since it is always measured at right angles to the 

 plane of equal intensity through the point. 



Several different types of gradient-field can be distinguished. 

 The scalar quantity may have a maximum at one end of the 

 system under consideration, and a minimum at the opposite 

 end. In this case the gradients have the same direction through- 

 out the field. This is called a linear gradient system, or, if the 

 direction of the gradient coincides with one of the axes of the 

 system, an axial gradient system (example: the temperature 

 gradient along an iron bar which is heated at one end, and 



