IN THE DIVIDING ROOT-TIP CELLS OF THE ONION. 29 



In order to prevent confusion in counting and classifying the cells, 

 which were viewed under the oil-inunersion lens, the field was divided 

 into quarters by means of hairs crossed in the eye-piece of the micro- 

 scope. Thus in a field containing from 50 to 100 cells it was easy to keep 

 one's bearings. No cells were counted twice, and all cells within a 

 selected field were counted and classified. 



Special attention is called to the Procession Index Tables (Nos, 12, 13, 

 and 14). In calculating the average absolute durations of the several 

 stages, only those waves were used which traversed in a definite manner 

 at least three-fourths of the stages of the entire mitotic cycle. Some 

 waves were cut off in their prime by the termination of the sampling at 1 

 p. m., and because the sampling had a beginning (namely, at 10 a. m.) 

 other waves were found already well advanced. The portions of waves 

 unused in the calculations are indicated by dotted lines. 



There are two blanks in these tables, one in the 20° series for the 

 sample at 11^50™ a. m., and the other in the 30° series for the 

 sample at 10^10™ a. m. These samples were duly taken and fixed, but 

 were ruined in preparation, so that while the results of the 10° series are 

 based upon the determinations of 19 samples of 1,000 cells each, in the 

 20° and 30° series each is based upon only 18 samples of 1,000 cells. 



In studying the results given in the several tables, attention is cglled 

 to the fact that, for better comparison between mitotically active and 

 mitotically inactive stages, in some cases the percentages are based 

 upon a cycle consisting of the 10 mitotically active stages only, omitting 

 the resting stage. In other cases the resting stage is considered as a 

 part of the mitotic cycle. Thus, in making comparisons other than 

 those set forth in the same tables, one must make sure that the data 

 apply to the same definition of the mitotic cycle. 



FURTHER DEVELOPMENT OF THE STATISTICAL METHOD. 



The results of the experimentation reported in this paper invite 

 future statistical investigations as follows: 



(a) To work out with more mathematical refinement the measure for 

 accuracy {prohahle errors) of the formulas here given. — This involves the 

 determination of the interrelation between the accuracy of the calcu- 

 lations and (1) the size of the individual samples, (2) the number of 

 observation-instants per series, and (3) the closeness of observation- 

 instants; and the working out, as hereinafter suggested, of a coefficient 

 of mitotic homogeneity or synchronization in the successive samples — 

 all of which would permit not only the calculation of probable errors for 

 the several determinations, but also would supply the basis for sound 

 judgment in planning experiments. For example, if only a limited 

 number of observations were feasible, it would enable one to choose, in 

 the interests of accuracy, between closer observation-instants covering 



