624 



RATE OF GROWTH OF DAIRY COW 



resultant of multiplication of cells, and the growth of the whole body 

 is the resultant of the interdependent and harmonious growth of the 

 various tissues. The whole body may therefore be said to be deter- 

 mined by a limiting autocatalytic reaction and as such the rate of 

 growth of the mass of the body should follow the velocity equation 

 of an autocatalytic monomolecular reaction. Robertson^ and Ost- 

 wald^ simultaneously but independently showed this to be the case. 

 The velocity equation of an autocatalytic monomolecular reaction 

 may be derived as follows: Let A be the amount of limiting growth 

 substance at the beginning of growth which is ultimately destined in 

 the presence of nutrients to be converted into tissue; let the amount 



dx dx 



Fig. 1. Curve of — = x(A — x). Ordinates represent velocity, — ; abscissae 



represent ascending values of x. 



SO converted be x] and, therefore, (A — x) remains unconverted. 



dx 

 By hypothesis, the velocity of growth — is proportional to both 



dt 



{A — x) and also to x which acts as the catalyzer of the reaction, that is, 



dx 



dt 



= Kx U - x) (1) 



^Robertson, T. B., Arch. Entwicklungsmechn. Organ., 1907-08, xxv, 581; 

 Biol. Centr., 1910, xxx, 316; Principles of biochemistry, for students of medicine, 

 agriculture and related sciences, Philadelphia, 1920. 



^ Ostwald, W., Vortrage und Aufsatze iiber Entwicklungsmechanik der Organ- 

 ismen, Leipsic, 1908, v, cited by Loeb (1910),2 and Robertson (1910).^ 



