10 DURATION OF THE SEVERAL MITOTIC STAGES 



and if corrections be made by means of the stage index for mitotic index 

 fluctuation and the size of the samples, the sunmaation of the percent- 

 age-frequencies (that is, of the stage indices) of a given stage in the 

 several successive samples will measure the average relative duration 

 (A. R. D.) of that particular stage. The one additional compHcation 

 (factor c) not present in the last hypothetical case does not change the 

 rule for this particular type {i. e., average) of measurement. Mathe- 

 matically stated, the formula for this determination is: 



S S. I. of the given stage in all 



Average relative duration (A. R. D.) ^ observations. 



of a given mitotic stage. s S. 1. of all stages included in the 



cycle, in the same fields. 



This equals also the average stage index for the particular stage in the 

 series of samples. 



Let us now consider the average absolute duration (A. A. D.) of the 

 several mitotic stages. If the mitotic index did not vary, but remained 

 constant throughout the day, and the coefficient of variabiUty for the 

 duration of stages of 'the same order were low, a single root-tip sample, 

 just as accurately as many samples, would supply data for measuring 

 the average relative durations of the several stages. The accuracy of 

 such measurements would vary with the square root of the number of 

 cells counted within the sample or samples. While such a condition 

 of constant mitotic index would, if it existed, greatly simplify the 

 determination of the average relative durations, it would debar entirely, 

 by the method herein used, the determination of the average absolute 

 durations of the several stages. 



It is fortunate, therefore, for the particular investigation in hand, 

 that such fluctuation in the mitotic index really exists in the growing 

 root-tip of the onion. For, in order to make this latter measurement 

 (A. A. D.), it is necessary first to trace through a succession of mitotic 

 stages and time-intervals a definite, recognizable mitotic wave. The 

 conditions conducive to an accurate measurement of the average abso- 

 lute duration of the several mitotic stages depend upon (a) the sud- 

 denness and greatness of change in the number of cells beginning the 

 mitotic process during the period of observation; (b) the greatness of 

 the number of such waves; (c) the greatness of the number of stages 

 traced through each individual wave (if fractional lengths of waves are 

 used and if they are not equally distributed over the whole cycle, they 

 must be applied only in determining the A. A. D. within their respec- 

 tive sections); (d) the greatness of distance apart of these waves, 

 especially if some of the stages involve a high percentage of the entire 

 cycle; (e) the approximation to constancy in durations of the mitotic 

 stages of the same order. 



\A^ile variations in none of these five factors would impair in the 

 least the determination of the average relative duration of the several 



