Angular number distribution in effusion is of concern to users of the Knudsen effusion cell, who frequently assume the validity of the Clausing theory. In this study a stationary surface-ionization detector in a high vacuum measured the angular number distribution of CsCl molecules effusing from a saturated vapor through a right-circular cylindrical orifice in the wall of a rotatable copper effusion cell. The variables were θ, the off-orifice-axis angle; D, the orifice diameter; L / D, the length-to-diameter ratio; and T, the effusion-cell temperature. Two orifices having D ≅ 0.28 mm were used, with respective L / D values of 0.49 and 1.3. For the short orifice, the range of p, the saturated vapor pressure, was 0.006–0.99 mm Hg, and that of T was 820°–1017°K; for the long orifice, p was 0.006–0.86 mm Hg and T was 820°–1010°K. At low T, where the Clausing theory was expected to be valid, the probability density P(θ), defined as the fraction steradian−1 effusing in direction θ, was in fair agreement with theory for θ > 35° for the short orifice and for θ > 20° for the long orifice. At θ near 0°, the largest deviations from the Clausing theory were observed. An unexpected deviation from theory was observed, namely, P(θ) at fixed θ showed fluctuation with the state of the gas. This fluctuation (1) had an L / D dependence, (2) was greatest at θ near 0°, (3) was least at θ near 45°, (4) was small but appreciable at θ near 90°, and (5) was reproducible upon cycling T and θ. High-pressure limits for molecular flow were found to be 2.1 > K (Knudsen number, ratio of mean free path to orifice diameter) >1.7 for the short orifice and 1.6 > K > 1.3 for the long orifice. In the transition region beyond the high-pressure limit of molecular flow, P(0°) decreased with increasing pressure for the long orifice, whereas P(0°) increased with increasing pressure for the short orifice, as did P(0°) for a near-ideal orifice.