410 THU AMERICAN NATURALIST [ Vol. LVl 



4) we solve tliem for p^, Pz and Pi, and obtain the values 

 shown in Table III. 



The seven values obtained give mutually consistent 

 values for the crossover percentages between the fifteen 

 pairs tested, and are therefore suitable for the construc- 

 tion of chromosome map. If the conditions of Maximum 

 Likelihood had been exactly fulfilled they would agree 

 better than any other consistent series of values with 

 the percentages observed. As it is, it is only in the ab- 

 errant value of ^7 that the assumption that the observed 

 values are approximately correct breaks down, and it 

 is probable that such cases will only occur when the data 

 are admittedly insufficient. 



TABLE III 



Table III is arranged to compare the differences be- 

 tween the calculated and the observed percentages with 

 the standard errors due to sampling ; except for p-, all the 

 differences are less than twice their standard errors ; thus 

 showing the general agreement between the data and the 

 theory of linear arrangement of the genes. The fit, 

 however, is not a close one, even if we omit p,; in the 

 present state of our knowledge this will not throw any 



