20 DURATION OF THE SEVERAL MITOTIC STAGES 



In which Po= percentage of cells dividing, Pi = percentage of cells 

 (dividing and active) in the same field, N= population of sample. The 

 determination of standards with which to compare such probable errors 

 would naturally be a part of any investigation seeking to develop a 

 coefficient of mitotic homogeneity. (See p. 30.) 



If a probable error could be calculated for each of the several stage 

 indices of these determinations, it would greatly simplify the calcula- 

 tions of such a measure for all of the subsequently calculated values, 

 because a stage index is an element in each of them. While the stage 

 index is of the same nature as the mitotic index, and normally should be 

 subject to the same probable-error formula, still it is not so easily cor- 

 rected, for, as a general rule, the values of the stages indices fall 

 below the critical point, namely, 5 or 6 per cent. 



The fundamental principles upon which the determination of this 

 study are based are demonstrably sound, but it is not possible, in the 

 present stage of biometrical science, to supply formulas which will 

 measure mathematically the approximation to the actual values of the 

 several calculated determinations. Some other common-sense method 

 of estabhshing our confidence in their degree of accuracy must be 

 applied; so let us continue by the comparative method to gage the 

 accuracy of the determinations of the hypothetical case, the preliminary 

 study, and the completer experimentations. 



It is quite evident that the determinations of the average absolute 

 duration will possess a greater relative error than do those of the average 

 relative duration, because the absolute value of a given stage is based, 

 (1) upon the absolute duration of the whole cycle, which itself is subject 

 to an error, and (2) upon the average relative duration of a given stage, 

 which also possesses an error. An element in reducing error in the 

 average absolute duration is the greatness of the number of waves 

 traced. In the hypothetical studies, in which temperatures were con- 

 stant, 6 waves were traced through the series grown at 10° C, 6 through 

 that at 20° C, and 7 through that at 30° C. 



Taking into consideration only the total populations of the samples, 

 we find that if the populations sampled be homogeneous throughout, 

 accuracy (or the approximation to the truth) is not directly a function of 

 frequency or numbers, but is a function of the square root of such fre- 

 quency. One must, therefore, if he would halve his approximation to 

 the truth, quadruple the quantity of his observational data. Since in 

 the preliminary study there were 13,000 cell-counts, or 18.35 times the 

 708 of the Method Chart, it is clear that if the data were taken from 

 a homogeneous population (which is not the present case) the determi- 

 nations based upon the 13,000 counts would in their approximation to 

 the truth deviate on the average only :;^== as far as those based upon 

 708 counts. In the final studies of this investigation, the first series 

 consisted of 19,000 counts, 26.77 times the number of the Method 



