THE probable errors of correlation coefficients are so often required that the accompanying abac which enables them to be determined at once will aave considerable labour. From this abac the probable errors can be read off correct to at least two decimal places; greater accuracy is seldom required. The principle on which the abac is constructed is simple. If we take the well-known formula for the probable error of a correlation coefficient where r is the correlation and n the-number of

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... ons, and express it in logarithmic form, we get log (£;)-r8289766+log (1 ^r 8 )-J log n. For any constant value of r there is thus a linear relationship between the logarithms of E T and n. Hence by plotting E r and n on logarithmic scales and ruling lines for a sufficient number of values of r, we can find E T from r and n without difficulty. The use of the abac can best be illustrated by an example. Let the correlation between -two variables be '35 and the number of observations 160; then to find the probable error of r, we must read along the perpendicular line from the number 160 on the scale of frequency until it crosses the diagonal line' representing a correlation of -55. The position of the point of intersection of these two lines is then read, by aid oi the vertical lines, on the scale of probable errors and the value "037 so obtained. After the diagram had been drawn in pencil, the whole of N the laborious work of ruling in the lines in ink and preparing the diagram for reproduction was undertaken by Miss H. G. Jones, and I have to thank her most heartily for her careful work.