126 VARIATION AND DIFFERENTIATION IN CERATOPHYLLUM. 



The second law of growth was stated in the following words (p. 106, 

 supra) : "As whorls are successively produced by a growing bud they 

 are formed with ever-increasing constancy to their type, the ultimate 

 limit towards which the process is tending being absolute constancy." 



This means that there is a steady diminution of variability accom- 

 panying the repetition of the morphogenetic process of whorl production. 

 As has been indicated in the preceding section of the paper, the same 

 rule holds with reference to branch production. 



The two laws evidently have one important point in common, namely, 

 they both express the fact that the form or character of a structure 

 produced at any point on the plant is in part directly related to or 

 determined by the previous morphogenetic history of the individual. 

 Successively formed structures develop in such a way that from a purely 

 objective point of view it appears as if the growing point on any axis 

 were influenced in its formative activities by the previous "experience" 

 through which the protoplasm of which it is composed has passed. 

 Especially is this true with respect to the phenomena embodied in the 

 second law. As has been shown above (p. 107) , in the detailed discussion 

 of this law morphogenetic products are progressively "better" formed, 

 that is, closer to type, with each successive production. The theoretical 

 importance of the demonstration of such a law of morphogenesis is 

 evident. 



It is the belief of the writer that both of these laws which have been 

 demonstrated for Ceratophyllum have a wide generality in other organ- 

 isms. From considerations of space it is impossible here to present 

 detailed evidence for this belief, but a few points may be very briefly 

 mentioned. We may consider each of the laws separately. In attempt- 

 ing to form an idea as to how generally a logarithmic law holds in the 

 growth of other organisms than Ceratophyllum, we are unfortunately 

 met at once by the difficulty that there have been comparatively f ew 

 quantitatively exact studies of growth ever made. Furthermore, it is 

 to be noted that so far as is known to the writer, there has hitherto 

 been no extended study of exactly the same phase of the growth problem 

 as that with which we have here dealt. In the present investigation 

 we have dealt with what may be called intra-individual or organal 

 growth, that is, with the growth differentiation of a series of successively 

 produced, generally "like" organs of the same individual. In contrast 

 to this previous studies of growth have usually dealt with what may be 

 called individual growth, that is, with the growth change in the same 

 organ or character in successive stages of life history of the individual 

 or individuals. The two points of view stand to each other in the same 

 relation that intra-individual variation does to intra-racial variation. 



