116 AGRICULTUEAL AND INDUSTRIAL BACTERIOLOGY 



determine by means of a stop watch the length of time 

 required for cell division or the length of the generation 

 time. Methods of counting, however, have been devised so 

 that we may know the number of living bacteria present in 

 a cubic centimeter of liquid at the beginning of any definite 

 period of time and the number at the end of that period. 

 From this it is possible to calculate the length of the gen- 

 eration time as follows : let n be the number of cell divisions, 

 that is, the number of generations which develop during a 

 given time, which we may represent by t. If we start with 

 one organism we shall have at the end of one generation 

 period two organisms, and at the end of the second genera- 

 tion period four organisms, and at the end of third period 

 eight organisms. It is apparent, therefore, that the number 

 of organisms originating from a single cell will be at the end 

 of the first period 2^, at the end of the second 2^, at the end 

 of third period 2^, and at the end of the «"* period 3". 

 If instead of beginning with a single organism we start 

 with any number, which we may represent by B, the number 

 at the end of the w'" generation period will be 



B 2" 



If we let the number of bacteria after time t be represented 

 by 6 we have the equation 



b=B 2" 



If this equation is solved for n it will be found that 



_ log b— log B 

 "~ log 2 



It is evident that the number of generations which will 

 develop in time * will be equal to the total time divided by 

 the generation time, that is, 



t 



