368 
MR. R. A. FISHER ON THE MATHEMATICAL FOUNDATIONS, ETC. 
the scope of the new process, the theory of the estimation of micro-organisms by the 
dilution method is investigated. 
Finally it is a pleasure to thank Miss W. A. Mackenzie, for her valuable assistance 
in the preparation of the diagrams. 
References. 
(1) K. Pearson (1920). “ The Fundamental Problem of Practical Statistics,” ‘ Biom.,’ xiii., pp. 1-16. 
(2) F. Y. Edgeworth (1921). “ Molecular Statistics,” ‘ J.R.S.S.,” lxxxiv., p. 83. 
(3) G. U. Yule (1912). “ On the Methods of Measuring Association between two Attributes.” 
‘ J.R.S.S.,’ lxxv., p. 587. 
(4) Student (1908). “ The Probable Error of a Mean,” ‘ Biom.,” vi., p. 1. 
(5) R. A. Fisher (1915). “ Frequency Distribution of the Values of the Correlation Coefficient in 
Samples from an Indefinitely Large Population,” ‘ Biom.,” x., 507. 
(6) R. A. Fisher (1921). “ On the ‘ Probable Error ’ of a Coefficient of Correlation deduced from a 
Small Sample,” ‘ Metron.,” i., pt. iv., p. 82. 
(7) R. A. Fisher (1920). “ A Mathematical Examination of the Methods of Determining the Accuracy 
of an Observation by the Mean Error and by the Mean Square Error,” ‘ Monthly Notices of R.A.S., 
lxxx., 758. 
(8) E. Pairman and K. Pearson (1919). “ On Corrections for the Moment Coefficients of Limited 
Range Frequency Distributions when there are finite or infinite Ordinates and any Slopes at the 
Terminals of the Range,” : Biom.,’ xii., p. 231. 
(9) R. A. Fisher (1912). “ On an Absolute Criterion for Fitting Frequency Curves,” ‘ Messenger of 
Mathematics,’ xli., p. 155. 
(10) Bayes (1763). “ An Essay towards Solving a Problem in the Doctrine of Chances,” ‘ Phil. Trans.,’ 
liii., p. 370. 
(11) K. Pearson (1919). “ Tracts for Computers. No. 1 : Tables of the Digamma and Trigamma 
Functions,” By E. Pairman, Camb. Univ. Press. 
(12) K. Smith (1916). “ On the ! best ’ Values of the Constants in Frequency Distributions,” ‘ Biom., 
xi., p. 262. 
(13) K. Pearson (1914). “ Tables for Statisticians and Biometricians,” Camb. Univ. Press. 
(14) G. Vega (1764). “ Thesaurus Logarithmorum Completus,” p. 643. 
(15) K. Pearson (1900). “ On the Criterion that a given System of Deviations from the Probable in 
the case of a Correlated System of Variables is such that it can be reasonably supposed to have 
arisen from Random Sampling,” ‘ Phil. Mag.,’ 1., p. 157. 
(16) K. Pearson and L. N. G. Filon (1898). “ Mathematical Contributions to the Theory of Evolution. 
IV.—On the Probable Errors of Frequency Constants, and on the influence of Random Selection on 
Variation and Correlation,” ‘ Phil. Trans.,” cxci., p. 229. 
(17) R. A. Fisher (1922). “ The Interpretation of x“ from Contingency Tables, and the Calculation 
of P,” £ J.R.S.S.,’ lxxxv., pp. 87-94. 
(18) K. Pearson (1915). “ On the General Theory of Multiple Contingency, with special reference to 
Partial Contingency,” ‘ Biom.,” xi., p. 145. 
(19) K. Pearson (1903). £ ' On the Probable Errors of Frequency Constants,” ‘ Biom.,’ ii., p. 273, 
Editorial. 
(20) W. F. Sheppard (1898). “ On the Application of the Theory of Error to Cases of Normal Distribu¬ 
tion and Correlations,” £ Phil. Trans.,’ A., cxcii., p. 101. 
(21) J. M. Keynes (1921). “A Treatise on Probability,” Macmillan & Co., London. 
