IN THE DIVIDING ROOT-TIP CELLS OF THE ONION. 17 



in both the preliminary and the fuller investigations reported in this 

 paper. 



The governing maxim in these studies has been: A maximum of 

 biology and a minimum of mathematics. Continual recourse was had 

 back to actual biological fact. Biometrical formulas mathematically 

 derived are mathematically correct, but if in course of their develop- 

 ment a single false biological factor enters, all subsequent derivations 

 are false. Full cognizance of this danger is in mind as the accompany- 

 ing principles and formulas are set forth. They are nevertheless pre- 

 sented with the confidence that they are sound, both biologically and 

 mathematically. We may safely say that although we can not see the 

 mitotic details in actual process of transformation we may determine 

 the average duration of the successive mitotic stages with fully as great 

 accuracy as would be possible if we were able to follow the normal 

 and unhampered mitotic train directly with our eyes (see charts 1 

 and 6). 



The work of developing the statistical method of interpreting from 

 dead material the facts concerning stage duration in live material and 

 that of conducting a series of preliminary cytological experiments were, 

 of necessity, carried on at the same time; for thus only could these two 

 phases of the investigation mutually suggest and correct. The work 

 was undertaken with the feeling that there must exist a definite mathe- 

 matically determinable relation between the number of cells found in a 

 given mitotic stage at a given time and the relative duration of that 

 particular stage. The purpose was to find, demonstrate, and formulate 

 such relationships. 



To begin the work the only thing to be done was to count and classify 

 the cell-stages in comparable samples of mitotically homogeneous 

 tissues killed in successive order. So far as development of the sta- 

 tistical interpretation was concerned, it was possible only to construct 

 charts and diagrams plotting different hypothetical condition-com- 

 plexes in reference to mitotic activity, and then inductively from these 

 to work out the mathematical properties of each factor contributory 

 to the complex relationship between the cell-counts as distributed among 

 specific stages and the average and absolute durations of their respec- 

 tive stages. Unless, indeed, one can see and retain in mind the set of 

 comphcations involved in each different situation, it would seem that 

 such plotting and coordinating of situations in accordance with known 

 biological facts constitute the only safe method of procedure in devel- 

 oping formulas adequate to solving this particular problem. The 

 properties and usefulness, for the end sought, of several of these situa- 

 tion-complexes are summarized in an accompanying table (No. 2) bear- 

 ing the title ''Properties of four condition-complexes in reference to 

 mitotic indices and stage durations." These are way stations reached 

 in seeking the final solution. 



