102 MR. W. F. SHEPPARD OR THE APPLICATION OF THE THEORY OF 
18. Error in mean, mean square, &c. 124 
19. Error in class-index.125 
20. Mean squares and products of errors in case of two attributes. 126 
21. Test of independence of two distributions. 128 
Part III.— Application to Normal Distributions. 
22. Pi’obable errors in mean and in semi-parameter by different inetliods.130 
23. Relative accuracy of the different methods. 132 
24. Test of hypothesis as to normal distribution. 136 
Part IV.— Application to Normal Correlation. 
(1 ) Correlation-solid of Two Attributes. 
25. Correlation-solid in general ... . 138 
26. Correlation-solid for normal distributions.139 
27. Determination of divergence by double median classification. 140 
28. Calculation of table of double classification. 141 
29. Differential relation of V and D. . . 146 
(2.) Application of the Theory of Error. 
30. Probable error in divergence, as obtained by different methods.147 
31. Relative accuracy of the different methods .... .150 
32. Test of hypothesis as to normal correlation.151 
Tables. 
Table I. Oi'dinate of standard normal curve in terms of abscissa.153 
Table 11. Abscissa of standard normal curve in terms of ordinate. 155 
Table III. Ordinates of curves of divergence-diagram in terms of abscissa.156 
Tabic IV. AbscissiB of curves of divergence-diagram in tex’ms of ordinate.157 
Table V. Table for calculation of probable error.159 
Table VI. Abscissa of standard normal curve in terms of class-index.167 
Introductory. 
In his ‘ Lettres snv la Tlidorie des Probabilites ’ (1846), Quetelet has shown 
that in certain anthroiiometrical statistics, e.g.., in statistics of height or of chest- 
ineasnrement, the curve of frequency is approxiinatel}’’ of the same form as the curve 
known to mathematicians as the curve of error,” hut better described for statistical 
purposes as the normal curve. A similar conclusion has been arrived at by later 
observers with regard to a large number of biological measurements. The general 
similarity thus established has been extended, primarily by Mr. Francis Galton, to 
certain cases of statistical correlation of two or more attributes. It has been tbimd 
