290 PRINCIPLES OF GENERAL PHYSIOLOGY 



no satisfactory evidence that the nutrition of the tissues is directly affected 

 thereby. 



On the other hand, the work of Head and Campbell (1900) on Herpes Zoster 

 requires consideration. This disease results in the formation of blisters on the 

 skin in the area of distribution of particular nerves. It was shown by the 

 investigators named that these changes in the skin are caused by irritative 

 changes in the dorsal root ganglia (see Fig. 77). Owing to these changes, 

 abnormal impulses are sent in an efferent direction along the sensory fibres 

 to the skin. Although I have been able to show (1901, 2) that dilatation of 

 blood vessels in the skin is produced by excitation of the sensory fibres of 

 dorsal roots, it seems difficult to believe that mere vascular dilatation should 

 cause the actual formation of blisters. At the same time, the possibility has 

 not been disproved. 



MATHEMATICAL LAWS OF GROWTH AND OF METABOLISM 



It might be supposed that such complex processes as those discussed in the 

 present chapter would be impossible of attack on mathematical lines. There 

 are, however, some encouraging results which require brief reference. 



Slator (1913) has shown that the growth of yeast can be expressed by a 

 logarithmic formula. If a culture medium be inoculated with N cells of yeast per 

 cubic centimetre, the rate of growth at a given moment of time is proportional to 

 the number of cells present at that time, that is N + n, where n is the increase in 

 number during the time which has elapsed since the inoculation. This is 

 clearly a case of the " compound interest " law, which was explained on page 36 

 above, and the simplest assumption that can be made is that the increase in 

 number is in direct linear proportion to N -f n, that is : 



where K is some numerical constant. 



On integration, this equation becomes : 



It might be supposed, not unnaturally, that this simplest formula would be 

 found to be insufficient, but Slator has shown by four different methods that it 

 does actually express the results until nearly the end of the period of growth, at 

 which time the food supply becomes restricted and the products of the reaction, 

 metabolites, commence to inhibit. 



The four methods used were : (1) counting the cells directly, (2) the rate of fermentation 

 by measurement of the rate of formation of carbon dioxide, (3) the growth constant, K, is 

 estimated by counting the number of cells and the rate of fermenmtion while the time is 

 eliminated, and (4) by comparing the time taken for two cultures, inoculated in a known ratio, 

 to arrive at some definite stage. In malt extract, with a small amount of hops, it was found 

 that the time taken to double the number of cells was 2*9 hours (see also the work of 

 Horace Brown, 1914). 



Even in the metabolic processes of the higher animals, we have already seen 

 reason to regard the operation of the law of mass action as being uninterfered 

 with, more especially where we know the reaction to be reversible. An interest- 

 ing instance of rate of reaction being proportional to the concentration of the 

 substances reacting is to be found in a paper by Hoesslin and Lesser (1911, p. 

 356). If a fasting dog is fed with meat, the nitrogen excretion is 14 to 15 per 

 cent, greater if it is given all at once, than if the same total amount is given in 

 six separate doses, at intervals of three to four hours. 



The Mendelian Laws of Heredity will be referred to presently. 



PHYSIOLOGICAL PROCESSES OF* THE LOWER ORGANISMS 



The fundamental processes of life in all organisms are, no doubt, similar, so 

 that it appears to be held by certain investigators that, on account of the 



