Results of computations with two different published expressions for the aperture averaging factor, theta, that gives the effect of a finite diameter receiving aperture in reducing the variance of a fluctuating light signal. Fried's equation makes use of the Rytov approximation to compute the log-amplitude covariance; for moderate turbulence, it can be valid only for a critical distance of the order of a few kilometers at optical wavelengths. Yura's expression is in agreement with Fried's up to the critical distance, and the theta tends toward a limiting value. The aperture averaged standard deviation tends to a limiting value for long propagation paths, while Fried's increases without limit. (Prepared for the [Journal of the Optical Society of America].) 8 pp. Refs.