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A mathematic81 formula for determining the sampling frequency on the bash of the eoefficiente of variation of the various parametera of interest of water quality is developed.The uncertainty or the variability of each sampling program is expressed M a fnnction of the sampling deaign variable in order to construct a performance index which will enable one to select. the beat sampling program. The notion of information content is used BB a beeis for the performance index.Under certain circumstences, the information content of a single composite in more than that of a single grab sample. However, the average of a series of grab samples provides more information than the average of a series of composite samples. This happens because the individual information content (entropy) of discrete portions of the composite sample are confounded in the average.It in shown that if the variability of the proportions is greater than the upper limit (provided in Table2), the information content of the composite, where the volume of each diecrete portion is collected h, proportion to the rate of flow (or discharge) at the time it is collected, is much smaller than that of the same number of grab samples or composite samples collected at constant volumeconstant time intervals.Time constant, volume proportional-to-flow since last sample compositee have the aame disadvantages.

Starting with the second Lagrange expansion, with f(z) and g(z) as two probability generating functions defined on nonnegative integers such that g(0) 0, we define and study a new class of discrete probability distributions called the Lagrange distributions of the second kind. This class has the probability function:z=O for y =0, 1, 2,.... Different families are generated by various choices of the functions f(z) and g(z). Families of the weighted distributions that correspond to the Lagrange distributions of the first kind are defined using different weight functions. For a particular form of the weight function, it is shown that, under some conditions, the weighted distributions of the members of the Lagrange distributions of the first kind belong to the class of the Lagrange distributions of the second kind. Weighted distributions of the Borel-Tanner distribution, Haight's distribution, generalized Poisson and generalized negative binomial distributions, etc., are shown to be the members of the class of Lagrange distributions of the second kind. Certain properties of the Lagrange distributions of the second kind are given.