OSTERHOUT— DYNAMICAL THEORY OF ANTAGONISM. 537 



attained). For convenience we assume that at equilibrium the con- 

 centration oi M (which we call 3;) is equal to 0.2951 and that the 

 net resistance (expressed as per cent, of the net resistance in sea 

 water) is equal to 3053' + 10, the 10 being added because at death 

 the resistance drops to 10 per cent. {i. e., the resistance of the dead 

 tissue is 10 per cent, of that of the living). The resistance in sea 

 water will therefore be (.2951 X 305) + 10= 100 per cent. 



Let us assume that the velocity constant of the decomposition of 

 M in sea water is .540. If the velocity constant of the reaction 

 A^>M is one thirtieth as great (.540-^-30= .018) the concentra- 

 tion of A must be 30 times as great as that of M in order to keep 

 M constant. Hence the concentration oi A (which will be called 

 x) must be .2951 X 30 = 8.853. 



On transferring from sea water to such a mixture as 65 NaCl -\- 

 35 CaCL we assume that the production of A ceases while the de- 

 composition of A and M go on at an altered rate, the velocity con- 

 stant for A^M being changed to .000481 and that of M^B to 

 .00859. We can now calculate the value of y at any subsequent 

 time, T. 



The value of y at the start is .2951 and this will decrease (by the 

 ordinary monomolecular formula) in the time T to 



y= .295i(e-^'=0. 



In this formula e is the basis of natural logarithms and Ko is the 

 velocity constant of the reaction M-^B, which results in the de- 

 composition of y. 



The value of x at the start is 8.853 • this will produce during 

 the time T a certain amount of y part of which will be decomposed. 

 The amount remaining at the end of the time T is given by the 

 formula' 



y = .^.^S2>[-~^){e-'''' - e-^-^'), 



" Rutherford, E., " Radioactive Substances and their Radiations," 1913, 

 p. 421. The values e-^^"^ and c-KiT may be obtained from Table IV. in the 

 Smithsonian Mathematical Tables, Hyperbolic Functions, by G. F. Becker 

 and C. E. Van Orstrand, 1909. See also Mellor, J. W., " Chemical Statics and 

 Dynamics, 1909, pp. 16, 98, 118. 



