SECT. 2] AND WEIGHT 415 



original data. Moreover, as a rational account this description of the 

 synthetic processes of growth is misleading, since (3) by this theory 

 the growth-rate is proportional to the increment gain in weight 

 regardless of the weight of the organism, or in other words, dis- 

 regarding the amount or concentration of the reacting substances. 

 (4) Figures for the growth of colonies as well as of individual organisms 

 are said to be described by autocatalytic equations and are classed 

 together. When growth is expressed in terms of percentage increase 

 in mass, however, the important distinction between phylogenetic 

 and ontogenetic growth is made evident ; for the former, after a short 

 latent period, in the presence of an experimentally modified environ- 

 ment proceeds at a constant rate [cf Richards], while the latter 

 does not. The S-shaped curve is the result of a limited and unre- 

 freshed culture medium. The individual organism, however, instead 

 of maintaining a constant growth-rate shows from the beginning 

 considerable negative acceleration. (5) The S-shaped curve is not 

 specific, for there are some physico-chemical processes not considered 

 to be autocatalytic which are described by a similar curve. Finally, 

 and this is the main objection, (6) chemical diflferentiation is not taken 

 into account by the autocatalytic theory, which is based on the con- 

 ception that there is some one master monomolecular reaction, 

 which, being the slowest of the chain of reactions concerned in the 

 phenomenon of growth, determines the velocity of the entire process. 

 As there is no direct way of measuring the product of the master- 

 reaction, the increase in the body-weight of the whole embryo is 

 taken to represent the product. In view of the marked changes in 

 chemical constitution which take place in the tissues with age there 

 is no reason to suppose, and in fact it is extremely unlikely, that the 

 total weight can be taken as an index of the amount or concentration 

 of any one chemical substance". The tendency that has existed in the 

 past to take the simple weight of the embryo as the sign par excellence 

 of its developmental stage and its "aliveness" is only another case 

 of the reluctance to judge by "ensemble", as Broca called it, instead 

 of by single indices, which was so long the bane of physical anthro- 

 pology. In this case, it is the increasing application of chemical 

 methods to the embryo which has shown the superficiality of regarding 

 mere weight as the pre-eminent factor. Lotka has drawn attention 

 to this point of view, and is inclined to compare embryonic growth 

 to the growth of a population such as Pearl & Parker have studied 



