12 DURATION OF THE SEVERAL MITOTIC STAGES 



trace the wave much as one follows a mountain range, with consid- 

 erable certainty, but not expecting each successive peak to reach a 

 uniform altitude. In this connection the critical student will examine 

 the procession index tables (Nos. 12, 13, and 14) with the greatest 

 care. He will satisfy himself concerning the definiteness — i. e., the out- 

 standing clarity and unbranching continuity of the waves as indicated 

 by the connecting lines. Also he will seek especially to determine 

 whether the absence of data for observation-instant number 12 in the 

 20° C. series and for number 2 in the 30° C. series impairs or destroys 

 the possibihty of accurate range-tracing. 



Theoretically, the proper correction of the stage-length, in order to 

 eliminate the difference due to variation in the duration of the several 

 stages, would consist in subtracting from an increased stage index of a 

 given stage, at a given instant of observation, the stage index of the 

 same stage for the next previous observation-instant. Thus corrected, 

 the stage indices would provide a wave of procession indices passing 

 through successive stages and time-intervals and connected by points 

 registering the same magnitude. But such mathematical procedure 

 would be possible only in case the normal stage index (that is, of those 

 cells not in the new wave) of each stage in every sample were always 

 proportional to the average relative duration of its own stage. In 

 such a case the procession indices for all stages and time-intervals 

 not in the new wave would be zero, while those for the new wave 

 would be marked throughout by points of equal magnitude. It is 

 easily determined by the actual counting and classifying of mitotic 

 stages in onion root-tip cells that there exists no such condition as fol- 

 lows: Uniformity in the mitotic index for a considerable number of 

 minutes, then suddenly a much larger and a definite number of cells 

 begin to divide and progress in a thoroughly parallel manner to the end 

 of their several mitotic processes, then at the completion of mitosis, by 

 the suddenly increased number of cells, the mitotic index drops to 

 exactly the same level as existed before the sudden beginning of the 

 new wave. But rather, the facts are, in the material studied, that 

 the mitotic index rises and falls continuously and in small increments, 

 only occasionally presenting a major wave, and even then none too 

 easily recognizable. 



All this comphcates but does not prevent the location of definite 

 mitotic waves; but we have to be satisfied with a mountain-range 

 effect instead of a dead level in the corrected heights of the points 

 tracing such waves. The formula finally developed for the procession 

 index is not the subtraction-rule above referred to — the actual mitotic 

 complex in the material used precludes that — but is a ratio-rule which, 

 as demonstrated immediately hereinafter, accounts for all of the com- 

 plicating factors and gives the wave-effect sought. Mathematically 



stated, the formula for the procession index used is: 



s. I. 

 Procession Index (P. 1.) = . ^ „ 

 A. R. D. 



