IN THE DIVIDING ROOT-TIP CELLS OF THE ONION. 7 



the determinations derived from Table B depends wholly upon the 

 degree of their approach to the results obtained from the actual count- 

 ing and measuring of the diagrammed stage durations (Diagram A, on 

 the upper half of the chart). 



APPLICABILITY OF PLAN. 



Since we may, from the study of mitotically homogeneous tissues 

 reared under the same conditions and killed instantaneously at regu- 

 larly successive intervals, construct a table with all the mathematical 

 properties of Table B at the bottom of the Method Chart, but can not, 

 from directly observed timing of a mitotically active living tissue, plot 

 the details of stage-successions as is done in Diagram A at the top of 

 the chart, it is the immediate task to establish the reliability of meas- 

 urements calculated from statistical data, as in Table B, and to demon- 

 strate the general applicability of the principles and formulas used. 



It is evident that if one kills and mounts, in accordance with modern 

 histological practice, a tissue whose cells are actively dividing, the 

 relative numbers of cells found in the several successive mitotic stages 

 will be dependent upon two factors: (1) the percentage of cells actually 

 dividing at the instant of kilhng; (2) the mitotic progress each particu- 

 lar cell has made since it began to divide. 



If all mitotically active cells began to divide at exactly the same 

 instant, and all had made the same progress, then but a single mitotic 

 stage would be seen in the sample. If in, not a single tissue, but in 

 many tissues wherein mitosis had begun at the same instant and 

 had made the same progress, samples are taken at short time-intervals 

 (shorter than the duration of the shortest mitotic stage), it is evident 

 that, if the total counts per sample be equal, the summations of counts 

 of each of the several types of cells in the whole series of samples will 

 show the greater number of cells to have been killed while passing 

 through the longer stages, and similarly a lesser number during the 

 shorter stages. In such case it is further evident that if in the stage- 

 sequence there is a stage whose length is shorter than the time interval 

 between the observation-instants, it is possible that such a stage may 

 be missed in the sampling, and since under the conditions above referred 

 to all cells of the same sample are in the same mitotic stage, an in- 

 crease in the number of cells counted in the sample would not supply 

 a chance of including it, nor would such increase in the size of the 

 sample have any bearing upon its representative character. 



If, however, most of the cells had begun to divide at about the same 

 time, and had progressed about evenly, an observation early in the 

 process would reveal a relatively high number of early stages; simihrly, 

 a late observation would reveal a relatively large percentage of the 

 late stages. The term relatively is here very important, for the cell- 



