468 GROWTH 



Free and Bound Water. Reference to the table above (LXXXI.) 

 will make it clear that this change of water content with age refers 

 almost exclusively to the bound water (q.v.) which we saw in an 

 earlier chapter is held with extreme avidity by the tissues. 



In the later stages of growth and especially in the higher 

 mammals the ratio of water to solids tends to diminish. Inhibi- 

 tion of growth occurs when means are taken to prevent the 

 entrance of water. For example, Loeb put Tuhidaria and Ccri- 

 anthus, which live and grow in sea-water having about 3 to 3-5 per 

 cent, salts, into a more concentrated mixture. He found when 

 the concentration of salts in the water was 5-4- per cent, that 

 these organisms ceased to grow. The water-holding power of 

 the salt solution, i.e. the exosmotic property of the artificial sea- 

 water, balanced the inwards pull of the protoplasm. 



II. Normal Rate of Growth. 



(a) Weight. Brailsford Robertson has shown that the rate of 

 increase in weight follows a curve characteristic of auto catalytic 

 reactions, i.e. of reactions in which one of the resultant products 

 acts as a catalyst for the whole reaction. A simple example of a 

 reaction of this type may be found in the inversion of an aqueous 

 solution of cane sugar at 100° C. Part of the product of the 

 reaction (glucose and fructose) appears to undergo further decom- 

 position, giving rise to an unknown acid which accelerates the rate 

 of inversion. 



If X denote the amount of invert sugar formed during hydrolysis, 

 X will also be proportional to the amount of acid produced. Now, 

 by the ordinary compound interest law in which a function varies at 

 a rate proportional to itself — an exponential function^ — we have : 



hx 



1 ax 

 or, on integratmg, k = — log , 



QX (I- lC 



where k is a constant. 



As the result of a series of experiments on auto-inversion at 

 100° C, the value of k for this reaction has been put = 122 X 10"^. 

 With this value we can tell at any time after the inception of the 

 reaction just how much sugar has been inverted. Fin-ther, it 

 is obvious that, as the action proceeds, the velocity due to the 

 concentration of the original substance gradually decreases (i.e. 

 the ordinary mass action without the catalyst), while that due 

 to the concentration of the newly formed substance keeps steadily 

 increasing. Hence, there must, at a certain time, be a maximum 



