SECT. 2] AND WEIGHT 409 



yolk plus embryo as one growth-system. Now a fourth and very 

 large group consists of those who have been greatly impressed 

 with the similarity which some empirical growth-curves show with 

 the curve for a monomolecular autocatalytic reaction. This manner 

 of looking at the subject is associated mainly with the name of 

 Brailsford Robertson, who has in many papers and in a book specially 

 devoted to the matter put it forward as the most fundamental ap- 

 proach to growth. Robertson was not, however, the first to notice 

 the likeness. As early as 1899 it had been referred to by Errera, 

 and Ostwald a little later. According to Monnier, Chodat of Geneva 

 paid some attention to it in 1904. "One may regard growth, 

 as M. Chodat has suggested", said Monnier, "as a complicated 

 chemical reaction in which the living cell is the catalyst and the 

 substances present are water, salts, and CO2." Four years later (in 

 1908 on May 9) Ostwald's monograph on growth was published in 

 the form of an inaugural dissertation, and only ten days later 

 Robertson's first paper appeared in the Archivf. Entwicklungsmechanik. 

 Ostwald had treated the question in a rather unmathematical manner, 

 but had fully explained the nature of his hypothesis ; Robertson, on 

 the other hand, gave the S-shaped curve a detailed mathematical 

 treatment. " The carrying out of a progressive development in 

 time has in animals a single characteristic type; the rapidity of 

 the process begins at a low value, increases with the continuance 

 of the action and falls off again at the end, in other words the type 

 of curve is S-shaped." This was as far as Ostwald went, but he did 

 not fail to point out that the S-shaped curve was identical with that 

 of an autocatalytic or an autocatakinetic reaction. An important 

 point to note is that Ostwald's curves were all curves of absolute 

 weight — he did not in any instance plot increment curves. 



Robertson began by an explanation of the mathematical properties 

 of the autocatalytic curve. The differential equation characteristic 

 of the initial stages of an autocatalytic monomolecular reaction is 

 as follows : , 



-r = k-iX [a — x), 



which expresses in mathematical symbols the fact that the velocity 

 of the transformation is, at any instant, proportional to the amount 

 of material which is undergoing change and to the amount of material 

 which has already undergone change. If, however, the reaction has 



