Four subjects were asked to judge the position of the second of a pair of light flashes with respect to the first when the distance and the temporal interval between these stimulus points were varied systematically. The temporal intervals were .25, .57, 1.32, 3.03, 6.96, and 16.0 sec. Four conditions of observation were used: (a)Foveal observation of stimulus points presented on a brightly lighted screen with no control of the Ss'' fixations, (b) Peripheral observation of stimuli presented on a lighted screen with the Ss'' eye movements controlled by a fixation point 5 deg. to the right of the stimulus area. (c) Foveal observation of stimulus points presented in complete darkness, fixation not controlled. (d) Periphery observation in complete darkness, fixation controlled as in(b). The range of thresholds obtained was as follows: (a) Condition A gave the lowest thresholds, 2.2 to 11.6 min. of arc. (b) Conditions B and D gave approximately the same thresholds, from 7.4 to 14.2 min. of arc. (c) Condition C gave the highest thresholds, from 7.5 min. to 3 deg. 4 min. of arc. (d) The variability of the Ss'' judgments was inversely proportional to their precision. It is concluded that: (a) Two points can be discriminated in visual space with high precision even when the points are presented successively, separated by intervals of as long as 16 sec. (b) Discrimination is better when the points are presented on a clearly framed background than when they occur without visual reference points, as in the dark. (c) A single fixation point is as effective as a more complex visual pattern in maintaining the precision of judgments. For the longest temporal interval (T = 16.0 sec.) the fixation point eliminates the difference between foveal and parafoveal discrimination thresholds.