352 PHYSIOLOGY OF BACTERIA 



centration. This proportionality does not hold for the 

 lower pH range. Here, a much better agreement is 

 obtained with the square root of the 0H~ concentration . 

 From pH 9.1 — 12.4, it is satisfactory. This is a wider 

 range of pH than we had before, and even the values 

 for pH 7.5 are not entirely out of range. At pH 13, the 

 agreement does not hold at all. This proportionaHty 

 to the square root of the 0H~ concentration agrees with 

 the just mentioned data of Cohen's. 



Theoretically, n must increase at very low concentrations. There 

 is a limit for any poison below which it will not harm the cell; it might 

 even stimulate. In other words, K becomes infinitely small when C 

 is still measurable. The value for n is computed from the equation: 



n = 



If C2 becomes so small that there is no death, the death rate K2 



k\ 

 becomes 0, and 7- = «, and therefore n — w. The change of n 



K2 



from a definite number to infinite is not abrupt but gradual, as will 

 be seen from Fig. 41, p. 358, and from the calculations of n on p. 361. 

 This must be kept in mind when the concentration exponent is 

 determined ; it will be constant only beyond a certain limit. Reichel 

 (see p. 356) called this limit a and did his calculations by assuming 

 K = Ko{c - a)\ 



A number of concentration exponents have been 

 determined, and they are compiled in Table 110. They 

 are mostly computed from the concentrations by weight 

 though it would be more correct probably, in most 

 cases, to consider ionization. In some instances, both 

 ions will have a deleterious effect, while other com- 

 pounds are not ionized at all. The computation has 



