We report on the sensitivity of human observers with respect to the detection of transients in otherwise uniformly moving two-dimensional random-dot patterns. The target field is divided into two halfs that each contains a moving random-dot pattern. The patterns in the two halffields are mutually uncorrelated. Parameters are the average velocity and the difference-velocity for the two halfs. These velocities are both vectors that can be varied in magnitude and in their direction with respect to the border of the two halffields. In order to quantify the sensitivity of the visual system to such patterns, we added (linear addition) spatio-temporal white noise ("snow") to the pattern. Then the sensitivity is quantified by way of the threshold signal-to-noise ratio necessary to discriminate the composite pattern from a single smoothly uniformly moving pattern. The signal-to-noise ratio specifies the square of the ratio between the signal r.m.s. contrast and the r.m.s. contrast of the masking stimulus (spatio-temporal white noise or "snow"). The r.m.s. contrast of the complex pattern (signal and noise) is kept invariant. We find that the detection performance is independent of the direction of either the average of difference-velocity with respect to the border, and can be completely described in terms of a minimum requirement for the magnitude of the difference-velocity. The magnitude of the difference-velocity must exceed the magnitude of the average velocity in order to lead to a perceivable transient. In this formulation the Weberlaw for the detection of velocity transients in uniformly moving noise patterns is applicable to both differences in magnitude and direction of the velocities.