AUTO-CATALYTIC REACTIONS 



469 



velocity due to definite concentrations of a and iT. In an auto- 

 catalytic reaction this niaxiniuni velocity is reached when the 

 concentration of the newly formed substance is half the concen- 

 tration of the original substance, i.e. when x = a/.,. 



Do statistical results bear out the statement that growth is an 

 autocatalytic reaction ? In the following table (LXXXII.) is 

 given for comparison, the weight of the human body at various 

 ages, as found and as calculated from the assumption that the rate 

 of growth is autocatalytic. 



From these results we see that the agreement between observed 

 and calculated results is excellent in all cases where a sufficiently 

 large number of subjects have been weighed, except at age 15|, 

 where weight increases more rapidly than theory demands. 



A simple but empirical formula for obtaining " exjjected " 



weight is —— — , where A = conceptional age in years and m is a 



constant for each age (see Table LXXXIII. for values of m and for 



results). 



(b) Length. It was at first believed that the length curve was 

 of parabolic form of the equation y^ = a{x + b), but later and more 

 complete investigation has shown that this is untenable. There 

 is for each type of body a definite relationship between length and 

 weight, viz. : I = ■\/mw, w^here I = length in metres, w = weight in 

 kilograms, and m is a constant for each age (and each type). As 



A 3 



w = 



4-75m 



, therefore A = 4-75/3 or / 



4-75 



(Pfaundlcr.) 



