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PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES Volume 5 JULY 15, 1919 Number 7 EVIDENCE OF STREAM MOTION AFFORDED BY THE FAINT STARS NEAR THE ORION NEBULA BY ADRIAAN VAN MAANEN MOUNT WILSON OBSERVATORY, CARNEGIE INSTITUTION OF WASHINGTON Communicated by G. E. Hale. Read before the Academy, April 28, 1919 The increased accuracy which can be obtained in the determination of proper motions of the stars by long-focus instruments makes it necessary to take into account quantities which otherwise could be neglected. When the probable error of the motion in a coordinate becomes as small as 0.003 or 0004, we may no longer neglect systematic errors of this size or larger, if they can possibly be determined. In a discussion of the proper motions of 85 stars in the region. of the Pleiades,I photographed with the 80-foot focus of the 60-inch Mount Wilson reflector it was found that in the reductions the quadratic terms of the coordinates could not be neglected, notwithstanding the fact that the size of the field was only 24 by 30 minutes of arc. For this and other reasons it was suspected that by neglecting such terms in a former discussion of the proper motions of 162 stars near the Orion nebula,2 photographed with the 40-inch Yerkes refractor, we had not attained the best possible results. A new solution has therefore been made including the quadratic terms; the necessary corrections are of the same order as those for the Pleiades field and may not be neglected. The comparison reveals the relative efficiency for this kind of work of the long-focus reflector, which seems easily able to withstand a comparison with the refractor. The fact that we are here dealing with a field in which many of the stars must belong to the nebula, especially in the center of the plates, has its disadvantages, as well as its advantages, for, the motion of the nebula being small, we ca