IN THE DIVIDING ROOT-TIP CELLS OF THE ONION. 19 



total population of the several samples were the one controlling factor, 

 these findings would consequently be much more to be relied upon than 

 the total of 708 counts recorded in the Method Chart ; but in evaluating 

 the accuracy of these results it must be borne in mind that (a) the num- 

 ber of individual cell-counts, the greatness of which tends to increase 

 accuracy, must be considered; (6) the greater the number of stages into 

 which the mitotic cycle is divided the greater the chance of error; (c) 

 the greater the number of observation-instants the greater the accuracy 

 of the determination; and (d) the shortness of intervals between 

 observation-instants conduces to greater accuracy. 



PROBABLE ERRORS. 



These four factors all tend, in so far as their bearing upon accuracy is 

 concerned, in the directions above indicated, but their incorporation 

 into a single accuracy-measuring mathematical formula has not yet 

 been accompHshed. Indeed, none of the several probable-error formu- 

 las now used in biometrical study will apply here. In planning the 

 later studies cognizance was taken of the directions in which all of the 

 aforenamed accuracy-factors operate, and the conditions of experimen- 

 tation, so far as possible and feasible, were modified in accordance with 

 these teachings to make for greater precision in the determinations. 



The probable error is a measure of accuracy for certain classes of 

 data, but when (a) the data in hand are not from material homogeneous 

 throughout the sampling, or (b) the values involved fall below 5 or 6 

 per cent, or (c) if the absolute numbers of individuals in the several 

 classes of the series are low, the probable errors as now calculated are 

 not valid. 



The mitotic index is found by applying the following rule: 



. Number of cells dividing. 



Total number of cells (both resting and 

 dividing) observed in the same fields. 



In these studies on the duration of the several mitotic stages in onion 

 root-tip cells only the mitotic indices lend themselves to the usual 

 probable-error corrections. This is because they alone, of all ratio- 

 results here presented, are measured by high percentages derived from 

 relatively large numbers. But even in case of the mitotic indices each 

 probable error so calculated is comparable with no other like determi- 

 nation of the series, because in each case the material is characteristic 

 of a given time of day, i. e., of a given instant in the mitotic rhythm, and 

 of a given temperature — that is, the population is homogeneous in the 

 given sample only. Nevertheless, the probable-error formula appli- 

 cable in each particular case is : 



