2 REGENERATION 



itself in time for the following reason. Let us consider the point 

 a I and one minute element of surface next to it on each of the two 

 sides, aia2 and OiC. The minute elements of area adjacent to 

 point ai on the side OiC will continue to grow slowly, but the 

 element of area adjacent to point ai on the surface aia2 will 

 grow more rapidly. As soon as this latter element reaches the 

 level of aiC, it will, on account of the change in orientation, grow 

 with the minimal velocity characteristic of the old surface UiC. 

 The same will happen at the angle a2, so that the area aia2 is 

 being steadily diminished. This is indicated diagrammatically 

 in Fig. 3, where the inner polygon aia^hdc is the side of the 

 mutilated crystal at the beginning of the experiment, and the 

 middle polygon 030461^161 is the side some time later. The rate 



d 



Fig. 1. Fig. 2. Fig. 3. 



Figs. 1 to 3. — Diagrammatic representation of regeneration of mutilated 

 cubical crystal. Figure 1, size of the crystal before mutilation. Figure 2, 

 mutilated crystal (angle a replaced by area a\a-i). Figure 3, elimination of 

 the new area a\a-i by more rapid growth of this area. 



of growth is indicated by the distance of the new lines from the 

 old. The distance of a3«4 from 0102 is greater than that of azCi 

 from OiC, etc. As a consequence 0304 is smaller than aiao or, 

 in other words, the wound of the crystal is "healing." This 

 continues until the whole area 0102 created by mutilation has 

 disappeared again and the angle 05 is reached. In this case the 

 crystal has its old cubical form represented by the side a^h^diCi. 

 Hence the regeneration of the crystal is due to the fact that the 

 area a 102 (Figs. 2 and 3) created by mutilation is bound to 

 eliminate itself by the more rapid growth of its elements, caused 

 by the change in the orientation of the new surface through the 

 nuitilation.^ 



2. We will now pass in review briefly a few typical cases of 

 regeneration in living organisms. It is at once much more 



1 Masing, G.: Die Naturwissenschaften, p. 895, 1922. 



