646] THE SYSTEMATIC LOCATION OF GENES 411 



doubt on the scheme of linear arrangement, but will sug- 

 gest that the crossover ratios in this part of the chromo- 

 some were not constant in all the strains used to compile 

 the data. 



In estimating the Goodness of Fit of data of this kind, 

 may be calculated by summing the values of cP/(r^, as 

 in Table III Attention should, however, be called to 

 the fact that it has been recently shown (3) that in enter- 

 ing Elderton's Table we must put n' equal to one more 

 than the number of degrees of freedom, remaining after 

 we have fitted our unknowns to the data. In the present 

 case we have found 7 unknowns from 15 equations, leav- 

 ing 8 degrees of freedom, so that n' should be 9, and 

 not 16. 



In conclusion it should be noted that to be available 

 for the use of this process the crossover data should be 

 stated in the form in which it is given by Lancefif^ld and 

 Metz, in which the crossovers tabled between any two 

 genes do not include those experiments in which an inter- 

 mediate gene was under observation. The practice of 

 throwing together all the crossovers between two genes, 

 in order to improve the ratios between the more distant 

 points, causes the same crossover to appear repeatedly 

 in diflferent entries. The data are no longer the product 

 of independent experiments, and must be re-summarized 

 before reduction. 



KEFERENCES 



1. R. C. Lancefield and C. W. Metz. The Sex-linked Group of Mutant 



Characters in Drosophila wilistoni. American Natubaust, LVI, 

 pp. 211-241. 



2. R. A. Fisher. On the Mathematical Foundations of Theoretical Statis- 



tics. Fhil. Trans. A, CCXXII, pp. 309-368. ^ 



on the Calculation of P. Journal of Eoyal Statisti-cal Society, 

 LXXXV, pp. 87-94. 



