8 DURATION OF THE SEVERAL MITOTIC STAGES 



numbers of an observation-instant selected at random, when the mitotic 

 index has not been constant, depends (a) upon the number of cells in 

 the sample having begun mitosis previously to the observation-instant, 

 and (b) upon the mitotic progress each has made prior to the observa- 

 tion-instant. Thus, if a large number of cells had begun dividing at 

 about the same time, but sufficiently remote and properly timed to 

 bring each of them to a certain very short stage at the time of killing, 

 and also the same number of cells had begun dividing at a different 

 period of time, but properly removed so as to bring their mitotic pro- 

 gress to one of the longer stages at the instant of kiUing, the numbers 

 of cells actually counted in these two stages in this one sample would 

 be equal and would not, therefore, measure the relative duration of the 

 two stages. If, however, in closely related tissues behaving mitoti- 

 cally in exactly the same manner, a series of samples be taken, both 

 earlier and later than the sample above named, in the later samples the 

 earlier stages become rarer and the later more numerous, and vice 

 versa the earlier samples show a rarer number of the later stages and a 

 greater number of the earUer ones. 



But if cells of the tissues sampled had begun mitosis at different 

 instants throughout the cycle of the mitotically most advanced cells 

 sampled, at a random instant of sampling there would be found a con- 

 fusing variety of mitotic stages. This is the situation plotted, and 

 analyzed in the method chart, because (as previously stated) it approx- 

 imates most closely the actual mitotic condition in the growing root-tips 

 of the onion. As a matter of common knowledge, these differences are 

 known to represent a cross-section and instantaneous view of many 

 cells in varying stages of mitotic progress. Because in the plan fol- 

 lowed (a) the series of samples is fairly representative of the whole 

 mitotic sequence, and (b) the total number of cell-counts per sample, 

 regardless of the mitotic stage, is large and constant,^ an examination 

 of the method chart shows that even when the mitotic index (M. I.) 

 fluctuates greatly, and the successive stages are of varying durations, 

 these differences coincide and average so that throughout the sampling 

 the summation of the counts of a given definite mitotic stage measures, 

 in proportion to the total number of cells counted for all stages, the 

 average relative duration (A. R. D.) of this particular stage. Thus, 

 not only the duration of the stage but also the mitotic progress which 

 each cell has made up to the instant of sampling must be provided for 

 in any statistical analysis of mitotic progress. 



Further, if in this same set of mitotic conditions, sampling and 

 counting, the observation-instants are further removed from each 

 other than the duration of the shortest mitotic stage considered, it is 

 possible that the sampling may omit such stage altogether, but the 

 probability of its being included increases with the number of counts 



1 If not constant, correction can be made by means of the Stage Index (S. I.) (see p. 9). 



