IN THE DIVIDING ROOT-TIP CELLS OF THE ONION. 15 



The dotted line attempts successfully to follow a mitotic wave 

 through successive time-intervals and stages, as one may judge by 

 comparing the actual plotting of the stage successions in the diagram 

 with the wave traced in the table, for here the final correction (in addi- 

 tion to that of the S. I.), namely, that for variation in the average 

 relative duration of the several stages, is partially made. One may 

 glance at this diagram and with the eye readily trace the course of two 

 mitotic waves; first the complete wave (No. 2) in the middle of the 

 plot, and second, earlier than this one, what appears to be the ending of 

 another (No. 1). Then, comparing such actual waves with their 

 mathematical treatment in the table below them, one's confidence in this 

 statistical method of tracing mitotic waves is established, especially 

 since the later stages of the earUer wave overlap, in the same observa- 

 tion-instant, the earlier stages of the later wave. In counting and 

 classifjdng cell-stages in an isolated sample, this overlapping presents 

 hopeless confusion; in the diagram the counts of successive samples 

 begin to coordinate in orderly manner; but only in the procession 

 indices (P. I.) of the statistical table (B) are the analysis and reorgan- 

 ization of the mitotic pulsations definitely achieved. 



FORMULA FOR THE AVERAGE ABSOLUTE DURATION OF A 

 GIVEN MITOTIC STAGE. 



The locations of the waves having been established, the duration of 

 definite sections of the cycle is determined in each particular case by 

 counting the number of time units passed through by the particular 

 wave traced, and the average duration of a single stage by dividing the 

 number of time units by the number of stages the wave passes through. 

 In case sections of cycles are included in such determinations, they 

 must on the average equably cover the entire cycle, for in each case a 

 given section of a wave subtends its component stages which may be of 

 varying durations. The average is then made of these several determ- 

 inations. The average absolute duration for the cycle is calculated by 

 multiplying the number of stages in the cycle by the average absolute 

 duration per stage. The average absolute duration of a particular 

 stage is then determined by multiplying the percentage measuring the 

 average relative duration of the particular stage by the number of 

 time-intervals measuring the average absolute duration of the entire 

 cycle. Mathematically stated, the formulas for the average absolute 

 duration of the entu-e mitotic cycle and for a particular stage are: 



Average absolute durationi 

 of entire active mitotic I 

 cycle (A. A. D. of C.) ... J 



Time periods elapsing between two points 

 in a recognizable procession of P. 1 



No. of stages covered. 



No. P. 1. waves followed. 



Average absolute duration] 



of a given mitotic stage [■ = A. A. D. of C. X A. R. D. of S. 

 (A. A. D. of S.) J 



