16 DURATION OF THE SEVERAL MITOTIC STAGES 



MEASURE OF ACCURACY. 



Reverting once more to the Method Chart, we find that by actual 

 count and measure from the diagram, the average relative durations of 

 the five stages run: 0.3213, 0.2609, 0.2167, 0.0398, 0.1611. The same 

 measurement, that is, the average absolute durations of the several 

 stages calculated from the stage indices of Table B, are: 0.2912, 0.2843, 

 0.2171, 0.0352, 0.1719. Similarly, by actual count and measure from 

 the diagram, the average absolute duration of the stage series measures, 

 in tune-units: 13.84, 11.24, 9.70, 1.78, 7.66; a total for the cycle of 

 44.25; an average of 8.92. While the same measurements calculated 

 through Table B give: 13.32, 13.00, 9.93, 1.61, 7.86; a total of 45.74; 

 an average of 9.14. The close approximation in this test case, of 

 the series of results derived from the table to those calculated from 

 first-hand count and measure in the diagram, establishes the general 

 vaUdity of the principle followed and demonstrates that results secured 

 from such tables alone may be expected to approximate the truth 

 within a relatively small error, provided that the size and representa- 

 tive character of the sample and the closeness and number of observa- 

 tion-instants in an actual case are comparable (in relation to their 

 stage and cycle durations) to the same relations in the hypothetical 

 case. Or, presenting the principle in another manner, granted that the 

 diagram is correct (an exact picture of a representative sample actually 

 taken). Table B derived from it will approximate it in proportion to 

 the greatness of the number of observation-instants. Only by chance 

 would the determinations of the table and the diagram be exactly the 

 same. 



The relatively small fluctuation in the duration of average stage 

 length among the waves actually traced (see lower left-hand corner of 

 charts 12, 13, and 14) indicates a consistency in turn indicative of 

 accuracy in measurements and deductions. 



We know that if in an actual case we find a definite percentage of 

 cells in a given stage at a given observation-instant, and at the next 

 observation find this percentage changed, there is a net difference, but 

 just where in the interim between observation-instants each particular 

 cell-stage changed we do not know. The closeness of the observation- 

 instants tends to lessen the error due to this fact. 



The facts bring us again (see p. 7) to this: From the data secured in 

 observing homologous dead material killed at regularly successive 

 time-intervals, we can not plot an exact diagram of mitotic stage suc- 

 cession in a given cell ; nevertheless we can construct the exact anolog 

 to Table B (Method Chart) with all of its mathematical properties, 

 including its characteristic close approach to the actual facts. This is 

 what was done, and thus the data are supphed for the determinations 



