FACTORS MODIFYING GROWTH 471 



Some organisms when their size reaches a certain limiting value 

 tend to divide into two ecjual })ortions (Sach's Rule). Therefore, 

 one has to deal with an increase in number quite apart from 

 increase in individual size or weight. It has been proved by 

 numerous experiments that the increase in the ninnber of cells 

 follows the compound interest laiv, i.e. is an autocatalytic reaction 



To summarise : ^Vhen it is said that growth is an autocatalytic 

 reaction it is inferred that (i.) superimposed on the velocity of 

 reaction, which may be classed as chemical and is governed by 

 the law of mass action, (ii.) there is a variation in rate due to the 

 presence of a catalyst in one of the products of the main action. 

 The phases of such a reaction are, at least, four : 



(1) Ordinary velocity, proportional to the mass of the reacting 

 bodies. 



(2) After a short period the catalyst makes its appearance, and 

 the total rate gradually and steadily increases. 



(3) Certain limiting factors probably caused by the presence in 

 the blood (or in the sap of plants) of endocrinetes inhibit too rapid 

 a growth. 



(4) The accumulation of the products of the reaction produces 

 a tendency to cause a reaction in the reverse direction. That is, 

 arrest of growth and even negative growth may be produced. 



Quetelet, who was the pioneer of the statistical study of growth, 

 found that the rate of growth alters with age in a definite orderly 

 way, and the velocity curve may be divided into fairly well-defined 

 regions, each having a definite and characteristic slope, e.g. 



(1) From conception to about 3 lunar months the velocity is 

 low, about 2 cm. per month. 



(2) Period of rapid growth from 3 to 9 hmar months — 9 cm. 

 per month. 



(3) Rate almost equal to (1), i.e. 2 cm. per month from birth 

 to 3 years or so. 



(4) Slower, but still rapid growth in early boyhood. (Marked 

 quickening in teens (growing age).) 



(5) Period of arrest — full stature has been reached. 



(6) Somewhere about 50 years of age the period of negative 

 growth sets in. That is, the curve of growth and picture of velocity 

 follows point by point the velocity curve of a typical autocatalytic 

 reaction. 



III. Factors Modifying Growth. 



Chemical reactions may be profoundly altered by alterations 

 in external conditions, and, therefore, we may expect to find 



