35 



was possible to find the exact distribution of the discrepancy 

 between prediction and observation, and to render previous 

 methods more exact in other points besides that mentioned above. 

 In addition the true form of the distribution of the rej^^ression co- 

 efficients was established, for which approximate forms only had 

 been pre\iously a\ailable. 



IXMKKITANCK CORRELATIONS. 



XII. R. A. l^^isHKK. "On the Dominance Ratio/' I'roceed- 



ing-s of the Royal Society of lulinbur^^h, 1922. Vol. 



XLII. pp. 321-341. 

 The effects of selection on the inheritance correlations show 

 themselves in the dominance ratio. The value obtained from 

 human measurements are all close to ^, and this value is not 

 readily intellig-ible upon the simj^ler theory in which the effects of 

 selection are ignored. When selection is taken into account it is 

 demonstrated that the dominance ration will rise to ^, thus pro- 

 viding the final step necessary to bring the whole of the existing 

 correlation measurements in mankind itito harmony with the 

 Mendelian theory of inheritance. 



CROSSOVER RATIOS. 



XIII. R. A. FisiiER. "T]ie Systematic Location of Genes hy 



means of Crossover Observations." American 

 Naturalist, 1922. Vol. LVI. pp. -lOtMll. 



It is shown how the whole of the information supplied by 

 crossover observations may be utilised in determining a consistent 

 system of crossover ratios; the method is based upon that 

 developed in Paper No. IX. (see above), and the working is 

 analogous to that of a solution of least squares. 



ACCURACY OF BACTERIAL COUNTING. 



XIV. R. A. Fisher, H. G. Thornton, and W. A. Mackenzie, 



"Hie Accuracy of the Plating Metlwd of Estimating 

 the Densitv of Bacterial Populations." Annals of 

 Applied Biology, 1922. Vol. IX. pp. 325-359. 



As a rule, the accuracy of biometrical determinations must be 

 ascertained empirically from a statistical study of the observations ; 

 in certain cases, as has been shown in the theory of haemocytometer 

 counts, the law of variation may be calculated, and the accuracy 

 known with precision, provided the technique of the counting 

 process is effectively perfect. A study of the extensive bacterial 

 count data accumulated at Rothamsted by Cutler and Thornton, 

 using Thornton's agar medium, indicated that the same law of 

 variation, the Poisson series, was obeyed by the number of colonies 

 counted on parallel plates. Statistical tests were devised which 

 proved that, save for a small proportion of definite exceptions, the 

 necessary perfection of technique was effectively realised. In 

 studying the exceptional cases it appeared that these fall into two 

 classes : (i.) an abnormally high variation which, when investigated 

 experimentally, has been traced to certain bottom spreading 

 organisms isolated from soil from Leeds and from Rothamsted, 



