IN THE DIVIDING ROOT-TIP CELLS OF THE ONION. 11 



mitotic stages, the character of each is vital in finding the average 

 absohite duration. And, since the relative duration for all of the 

 several stages is so readily and accurately determinable, it suffices to 

 find only the average absolute duration for a few stages, whereupon 

 determining these latter durations for the whole cycle of stages is a 

 matter of simple calculation. This, also, is indeed fortunate, for, if 

 the waves were closer together than the time-period measuring the 

 duration of the longest mitotic stage, the curves marking their progress 

 would in the longer stages become inextricably tangled. The phenom- 

 enon of one wave running into another, thus destroying the recogni- 

 tion of the identity of both in their further progress, may well be called 

 jamming. Thus, in the studies made on the onion root-tip it was 

 found ad\dsable to eliminate (for the purpose of tracing definite waves, 

 but not for measuring the average relative durations) the resting stage, 

 which consumes a large percentage of the duration of the entire cycle. 

 In some cases even stage 1 (which, in the onion, when the growing 

 temperature was 30° C, was found to be of even longer duration than 

 the resting stage) may have to be eliminated in order to prevent 

 jamming, but, as was seen above, such elimination does not preclude 

 the determination of the absolute duration of a definite portion of the 

 mitotic cycle, and thence by simple calculation of each definite stage. 



PROCESSION INDEX. 



Throughout the actual studies on the onion, as in the Method Chart, 

 it was found necessary for the purpose of locating mitotic waves, to 

 calculate for each stage-count not only the stage index (S. I.), but also 

 a procession index (P. I.). The stage index corrects the deviations 

 from the actual wave-course in the stage index table in so far as such 

 are caused by differences in the size of the samples and by variation in 

 the mitotic index. Such correction lends itself directly to the purpose 

 of calculating the average relative durations, but it does not possess 

 properties enabling one, by connecting high values in a succession of 

 such indices (S. I.), to trace a mitotic wave through a succession of 

 time-intervals and stages in which the stage-lengths of different orders 

 vary to any considerable degree. It is necessary, then, for wave- 

 tracing purposes, further to correct the stage-index values by tak- 

 ing into consideration the average length of each stage into which 

 the cycle is divided. This correction is accomplished by means of a 

 Procession Index (P. I.). In order to secure this (i. e., the P. I.) for a 

 given count, the stage index (S. I.) is divided by the average rela- 

 tive duration (A. R. D.) of the particular stage. Thus cross-section- 

 ing partially corrects the differences in magnitude of the successive 

 values of stage indices in the path of the mitotic wave, due to the dif- 

 ferences in length of the several stages. The correction is complete 

 in latitude and longitude, but is only partial in altitude; it suffices to 



