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Recent measurements at the National Bureau of Standards, the University of Texas, the National Physical Laboratory, and elsewhere have indicated that the conventional constants ( K/mb, K) in the expression for the refractive index of moist air should be revised. Various laboratories appear to have arrived at this conclusion independently, with the result that there are at least four different sets of constants in current use. In much of propagation work, the absolute value of the refractive index of the atmosphere is of small moment. However, in some work it is important, and it seems highly desirable to decide upon a particular set of constants. It is also advisable to agree on the amount of future improvement in the constants which will make it worth while to respecify them. This paper attempts to give "best" values of the constants in the least squares sense and also suggests a criterion for deciding whether a future change would be worth while.