DELAYED EXPRESSION OF MUTATIONS 467 



giving rise to this population would also be'CN/(h — r). The mutation rate, a, 

 when one mutation occurs in this number of bacterial divisions is of course 

 given by the formula: 



a=(ln2)(h-r)/CN. (5) 



Mutation rate is very slightly underestimated by this formula, since r is an 

 overcorrection for the probable number of resistant cells from mutations sub- 

 sequent to the first. A more precise correction would be obtained by averaging 

 the number of resistant cells per culture, exclusive of those from the first mu- 

 tation in the series. This complication has not been introduced, however, since 

 the gain in accuracy would not be appreciable. 



The rates calculated in this manner may be considered as approaching the 

 true rate if most of the members of these older clones have become pheno- 

 typically resistant. If only a small proportion have become resistant, this rate 

 is still an underestimate, although it would be closer to the true rate of gene 

 mutation than the estimates using method 2. This method will be known as 

 method 5. 



The rates obtained in this manner, using the data from table 1, are presented 

 in table 8, together with the values required for the calculations. Data of 



Table 8 



Mutation rate of B/r to resistance to phage Tl, calculated from the maximum number of resistan 

 bacteria in any one culture of a series, using method 5 of this paper, and the data in table 1. 



experiment A B C D E F G H 



Number of cultures 

 Bact. per cult., X 10* 

 Av. resist, b. per cult. 



Max. no. resist, bact. 

 Mutation rate, XlO -8 



Luria and Delbruck, and Demerec and Fano, obtained using phage Tl, 

 have been treated similarly, and a detailed comparison is made in table 9 of 

 rates from methods 1, 2, and 5, using information from all sources. For the 

 sake of convenience, the rates obtained by methods 2 and 5 have been ex- 

 pressed in the last two columns of the table in terms of the smaller value from 

 method 1, as ratios— rate (2)/rate (1), and rate (5)/rate (1). 



Taking into consideration all available information on mutation to resistance 

 to phage Tl, rates from methods 2 and 5 differ only slightly and are between 

 four, and nine times the rates from method 1. 



The application of method 5 has also been extended to the data obtained 

 by Demerec and Fano using phages other than Tl; and averages of mutation 

 rates from methods 1, 2, and 5, and of the ratios rate (2)/rate (1), and rate 

 (5)/rate (1), have been worked out for all available data on strains B and B/r 

 and phages Tl, T3, T4, T5, T6, and T7. They are given in table 9. 



6o 



