46 Klllliui of Boti-jjtU Spores bjj Phenol 



only measure of resistance is the time taken to kill. But the times taken 

 to kill of the survivor curve will correspond to the grades of resistance 

 of the frequency curve, only if the reaction between spore and poison 

 is proceeding at a uniform rate in all the grades. The two curves will 

 agree only if it takes twice (3, 4 ... w times) as long to overcome 

 2 (3, 4 ... n) X grades of resistance as it takes to overcome x grades of 

 resistance. They will correspond only if RjT = Tc, where R is resistance 

 and T is time taken to kill. If this be not true, then it is illegitimate 

 to translate the survivor curve directly into a frequency. If the reaction 

 is proceeding faster in some grades than in others, if, e.g. it does not 

 take twice as long for the phenol to go through a coat twice the thickness, 

 but a time more or less than twice, then the times of dying do not accu- 

 rately give the grades of resistance, and the true frequency curve can 

 be derived from the survivor curve only by introducing some factor 

 which will compensate for the change of rate. 



This is the fallacy in the argument of those who object that the 

 J-shaped frequency is an impossible form here. They assume tacitly 

 and without evidence that the reaction is proceeding at a uniform rate 

 in all the grades. But it has been shown above that for Botrytis spores 

 at any rate this is not the case. As the strength of phenol is raised, the 

 reaction runs quicker, relatively, in the spores which die early than in 

 those which die late; and it is not a legitimate proceeding to transpose 

 the survivor curve obtained with these high strengths of phenol directly 

 into the frequency curve. What is got by so doing is not the real fre- 

 quency curve. To get at the real distribution of resistances as they exist 

 in the spores of the suspension it is necessary to introduce a compensating 

 factor which allows for the change of rate. 



What general form, applicable to all strengths of phenol, this factor 

 should take, it is not possible at present to determine. The fact that 

 we do get a nearly normal curve from the 0-4 per cent, survivor curve 

 shows that, for that strength of phenol, the reaction is running at a 

 nearly uniform rate in all the grades. If, however, with a sufficiently 

 high strength of phenol, the change in RjT takes some such form as 

 R/\og T = k, then we shall get from our original frequency curve a 

 survivor curve that is nearly normal, and from the logarithmic survivor 

 curve a frequency curve approaching normahty. 



To take an illustration: if we assume that the observed frequency 

 curve shown in Fig. 8 accurately expresses the actual distribution of 

 resistances in the spore suspension (it is not Ukely to be exactly accurate, 

 because it is not hkely that we have exactly hit off the correct strength 



