IN THE DIVIDING ROOT-TIP CELLS OF THE ONION. 21 



Chart, and consequently deductions from such data would be expected, 

 on the average, to vary only ;7^= as far from the actual values; but 

 other factors enter. 



In the hypothetical study 708 cell-counts were distributed among 27 

 observation-instants and 5 mitotic stages. In the preliminary study, 

 which was made on onion root-tips, 13,000 cell-counts were distributed 

 over 13 observation-instants, and classified among 11 stages (10 active 

 and 1 resting) ; while the final study consisted of a total of 55,000 cell- 

 counts divided into 3 subordinate studies, the first with 19,000 counts 

 and the second and third with 18,000 each. In the first the counts 

 were distributed over 19 observation-instants and among 11 (10 active 

 and 1 resting) mitotic stages; the second and third were each distributed 

 over 18 observation-instants and among the same 11 stage- types. As 

 was earlier pointed out, until all these factors have been joined in an 

 accuracy-measuring formula, we must be content to balance in judg- 

 ment the factors which later may be balanced mathematically and 

 with the highest efficiency. In our experimentations we can, there- 

 fore, in the interest of accuracy, only increase as much as feasible the 

 quantity of each type of data in the direction proven to make for 

 the reduction of error. 



OTHER SOURCES OF POSSIBLE ERROR. 



But it must not be concluded that all of the sources of error in a study 

 of this sort are traceable to lack of extreme refinement in statistical 

 methods. For instance, the matter of judging the individual cells and 

 classifying them into their previously determined stages is important, 

 especially since it is indeed difficult to draw a sharp line of demarcation 

 between the end of one stage and the beginning of another. Moreover, 

 in counting and classifying so many (55,000) cells, on the basis of 

 mitotic condition (10 active and 1 resting stage) there is a possible 

 source of error of interest both to biologists and psychologists; the 

 criterion for classification are apt to undergo evolution in the ob- 

 server's mind. This diflBculty was attacked by establishing the criteria 

 set forth in the three figures (see Summary Chart) for each stage marked 

 off. From the examination of these it will be seen that the difference 

 between the last condition of one stage and the first of its successor 

 is very slight and is determined in most cases by a single point of differ- 

 ence, the principle being to characterize these stages not by general 

 conditions descriptive of their means, but to set them off by clean-cut 

 lines. If error crept into the determinations because of this difficulty, 

 it would probably have come in between stages 1 and 2 — that is, where 

 the criteria for distinctions are the least well marked. We find in stage 

 1 but Httle acceleration in the 20° to 30° C. rise, while in stage 2 in the 

 same temperature rise we find the largest velocity increment in the 

 whole series. This compensating coincidence may lend color to the 



