IN THE DIVIDING ROOT-TIP CELLS OF THE ONION. 9 



per sample; and even in this case of very short stage-length, if the 

 sample be large, the stage-length is proportional to the summation of its 

 corrected counts. Unlike one of the hypothetical conditions earlier 

 described, wherein mitotic progress runs exactly parallel in all of the 

 mitotically active cells, in the present case of fluctuating mitotic indices 

 and variously beginning mitoses, the representative character of the 

 sample and the accuracy of the determinations are increased with the 

 number of cell-counts per sample. 



STAGE INDEX. 



The stage index (S. I.) simply casts into percentage the actual count 

 of each of the several mitotic stages observed in the sample. Thus, for 

 arithmetical purposes, correction is made for the population or size of 

 the sample and for fluctuation in the mitotic index, if the resting stage 

 be not included in the cycle. Mathematically the formula is stated as 



„^ T 1 /CI T \ No. of cells in given mitotic stage. 

 Stage Index (S. I.) = 



Total number of mitotically active 

 cells observed in the same fields. 



If in each sample the cell-count continues until 100 dividing cells are 

 counted, the stage-counts are directly proportional, each to each, to 

 the stage indices. If, however, the count be continued until 100 cells, 

 including the resting cells, are tallied, and the stage index refers to the 

 percentage of the cells actually dividing, i. e., if the resting stage be not 

 included in the cycle, then, as in the first treatment of the actual 

 studies presently to be set forth on mitosis in the root-tip cells of the 

 onion, such simple proportion does not hold good and the stage index 

 must be calculated for each count. 



MITOTIC STAGE DURATION AND TIME COMPLEX FOUND IN THE 

 DIVIDING ROOT-TIP CELLS OF THE ONION. 



Finally, we come to the actual complex of mitotic conditions found 

 in the growing root-tips of the onion, namely: (a) fluctuating mitotic 

 index, implying variation in the numbers of cells beginning and ending 

 mitosis at successive instants; (6) stage-lengths varying in successive 

 order in the same cell; (c) variations also among stages of the same order 

 in different cells; (d) closely parallel mitotic processes in different but 

 similarly appearing root-tips of the same bulb. 



FORMULA FOR DETERMINING THE AVERAGE RELATIVE DURATION 

 OF A GIVEN MITOTIC STAGE. 



Having determined the effect of each of these complicating factors 

 a, h, and c (factor d is treated on p. 13) upon the cell-count of successive 

 mitotic stages, and made corrections for each, we find that if samples 

 of tissues mitotically active as above described be taken at regular and 

 short intervals throughout at least a considerable portion of one cycle, 



