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In a previous papert the writer has called attention to a number of the interesting properties of the figuratrix in the calculus of variations. It is the purpose of the present paper to define a figuratrix for double integrals and to develop some of its important characteristics. 1. A new form of the problem of double integrals. The theory of extrema of double integrals has been treated for integrals of the form

Hadamard defines the figurative of the point (x, y) as the curve F(x', y') 1, where x' and y' are the current co6rdinates, and x and y are considered constant.t The polar reciprocal of the figurative with respect to the unit circle x'2 +y'2 = 1 is termed by Hadamard the figuratrix. The importance of the figuratrix and its space analogue seems to have been overlooked, and it is the desire of the writer to call attention to a number of their interesting properties which enable one to interpret geometrically some of the well known functions and theorems of the calculus of variations. 1. Figurative, figuratrix, and indicatrix. We shall prefer to consider an integral of the form

IT was the original purpose of this study to attempt to discover the effect upon the distribution in random samples, particularly in small samples, of the productmiioment coefficient of correlation, r, when the samples are drawn from a non-normal instead of a normal population. In Part I the results of sampling from certain populations which differ greatly from the normal are given, also the results of sampling from a normal population having a high degree of correlation. As the sampling was done experimentally, it was necessary to deal with discrete populations. This opened up the question of the effect of grouping upon the distribution of r, a question which is investigated in Part II.

(1917). An Intrinsic Equation Solution of a Problem of Euler. The American Mathematical Monthly: Vol. 24, No. 9, pp. 420-422.

(1922). The November Meeting of the Missouri Section. The American Mathematical Monthly: Vol. 29, No. 1, pp. 1-3.

LET X and s be the mean and the standard deviation respectively of a sample of n drawn from a universe having mean M and standard deviation a. Let x be the deviation, X M, of the mean of a sample from the mean of the universe. The ratio z = x/s (or t = z v/nn-1) plays an extremely important part in a number of statistical problems such as determining the probability that the mean of the sample does not deviate from the mean of the universe by more than a stipulated amount, comparing two mean values, and finding the sampling errors of regression coefficients*. The distribution of z for samples of n from a normal universe has been completely determined-originally by " Student," who applied it to the first of the problems just mentioned-and tables of the distribution for various values of n have been constructed.