6 DURATION OF THE SEVERAL MITOTIC STAGES 



sampling, one in which the mitotic stages may be definitely marked 

 according to arbitrary but fixed standards, and one which will yield 

 numerous samples in order that the average values calculated may 

 have relatively small probable errors. 



The method herewith presented is a statistical one based upon stage 

 counts and their classification, within selected microscopic fields taken 

 from closely related and similarly active tissues through a regular suc- 

 cession of observation-instants. The calculations and comparisons 

 shown on the accompanying Method Chart demonstrate the generality 

 and vaUdity, for the purpose designed, of the principle so based, and 

 which is employed in determining the measurements reported in 

 this paper. 



PROOF OF PRINCIPLE: HYPOTHETICAL CASE. 



The principle here employed is as demonstrable as a geometrical 

 theorem. For the purpose of such proof the case here first presented 

 (see L Method Chart) is an hypothetical one in which the mitotic prog- 

 ress is plotted for each of a series of related cells, through an evenly 

 graduated time-scale. Among the cells thus plotted there is fluctuation 

 in (a) the mitotic index^ (M. I.), (6) the duration of successive stages 

 within the same cell, and (c) the duration of stages of the same order 

 in different cells. This situation, as will be seen later, approximates 

 the actual condition of mitosis in the dividing root-tip cells of the onion. 

 Then transversely across the stage-duration diagram, and parallel to 

 the time-interval lines, are drawn at three time-intervals distant a 

 series of fines marking observation-instants. This graphical presenta- 

 tion of the stage-durations (A. Diagram plotting the situation) lends 

 itself to the actual counting of stages and to measuring their several 

 lengths, thus providing data adequate, by simple arithmetical calcula- 

 tions, to determine the average relative duration (A. R. D.) and the 

 average absolute duration (A. A. D.) of each stage type plotted. Also, 

 it makes possible the construction of Table B, which appears on the 

 lower half of the same chart. The data for this table are secured 

 solely by counting the different mitotic stages (including the resting 

 stage) at the successive periods passed through by the observation- 

 instant lines. From the data thus secured the average relative and 

 absolute durations of the several mitotic stages are calculated. 



It is evident that the calculations of the average relative and abso- 

 lute durations made from actual counting and measure are the correct 

 ones for the particular case presented. The general applicability of 

 the results thus obtained depends entirely upon the representative 

 nature of the sample used; but the reliance which we may place upon 



'Professor C. S. Minot first used and defined the term mitotic index, "Age, Growth, and 

 Death." Pop. Sci. Mo. 71: 510, 1917. It is the percent-measure of the total number of cells 

 showing mitotic activity in a given sample tissue. 



