the selected conditions the test-object was visible much below this lower limit; while, under others, its visibility was not attained even at the highest brightness available.

APPARATUS AND PROCEDURE

The apparatus was arranged as in the earlier work (1, 2). The test-object chosen was of the double bar type (b, Fig. 1),

FIG. 1. The test-object (b) and the pre- and post-exposure patterns (a and c). The test-object could be shown in the vertical position as well as in the horizontal. First a appears, then b, then c, in the same place. The unit-dimension in this figure is 3.18 mm. (inch).

and was exposed with confusion fields (a, c) immediately preceding and following it at the same point on the screen. The unit' is the nominal dimension hereinafter used to describe the stimulus-complex a-b-c. As before, the width of the bar and the width of the intervening space are each I unit, the length of the bars in the test-object b is 3 units and the diameter of the confusion-pattern 7 units; the stripes and the spaces in these latter being spaced exactly as the bars and spaces of the test object b.

Since the brightness was the experimental variable the objects were so made as to give the desired brightness relations when viewed by reflected light, in order to avoid the frequent independent adjustment of more than one lighting device. The central portion of the screen carried a mask, made of heavy tin, with a rectangular opening, 5 cm. wide and just equal in height to the diameter of the confusion patterns a and c. The test-object was centered behind this opening, as close as possible without interfering with the operation of the two gravity drops carrying the cards on which were drawn the pre- and post-exposure patterns. Of these, the pre

exposure pattern was drawn with its circular outline tangent to the upper edge of its card. This same edge of the card just coincided with the upper edge of the mask-opening in the initial phase of the exposure a, with the pre-exposure pattern therefore just centered in the opening. When the first (lower) drop was released, it carried the card with it out of sight below the lower edge of the opening, thereby exposing the test object b. During the next stage (exposure) the second (upper) drop, carrying the card with the post-exposure pattern tangent to its lower edge, rested with the lower edge of the card exactly at the upper border of the mask opening. When this second drop was released it fell, covering the testobject and coming to rest with the pattern centered in the opening. Rebound was prevented by means of a friction. stop. The plane of the test-object was 42 mm. behind the mask, which gave clearance sufficient for the drops to work between with perfect freedom.

The drops were each a small tray made of tin, with three sides only. This left one edge of the bottom free, which was the edge which worked between the mask and the test-object. The card carrying the pattern was in each case attached to the drop with small clips, which permitted ready removal and replacement, with the circular pattern-outline tangent to the free edge. The drops were provided with lugs which worked freely in grooves in a pair of vertical wooden guides. The release was brought about by a double-acting electromagnetic device, which rocked a suitable escapement, first in one direction releasing the first drop, then back, releasing the second. Two switches on the arc of a pendulum timed the two releases, and the second switch was adjusted to a position on the arc which would give the exposure-time desired. For the ad libitum exposures, the apparatus was arranged so that the second drop did not fall at all. The two drops were raised together by hand, and the pendulum was released by a key under the hand of the subject when he received the 'ready' signal.

The times of exposure selected were 500, 1000, 2000 and ad libitum (T). The experimental program consists of two

separate pieces of work, the second of which was not begun until after the completion of the first. The two sections involved the coöperation of two groups of subjects, composed in part of identical individuals.

I. At first, test-objects and confusion patterns were used which were made by simply drafting the patterns (a, b and c, Fig. 1) with India ink upon white card. The reflection-factor ratio, card to ink, was in this case 100: 4. Three sizes of these test-objects were used, the unit of the scale being 1, 2 and 3 mm. respectively.

II. It was desired to get corresponding data for testobjects having lower contrast than the above. The difficulties of preparing test-objects of this sort are many. First, a means must be devised of delineating a form which shall have a uniform reflection factor not greatly different from the ground upon which it shall appear. Secondly, this reflection factor, or at least its value relative to that of the ground, must be measurable and must also be reproducible for the other test-objects of the same series. Since the areas involved are small such measurement has to be made upon a large sample prepared especially for the purpose, and reproducibility becomes a factor of high importance. Thirdly, the effect upon the reflection factors of soiling has to be considered. The change in reflection factor of white and light gray surfaces, brought about by dirt and finger-marks, is surprisingly great; and the resulting change in visibility is presumably much more important than for the case in which the elements are originally white and black, although it is by no means negligible in the latter case.

The expedient finally hit upon consisted in the use, in place of card, of translucent white celluloid (3). The testobject and patterns were drawn with India ink upon sheets of this material 0.38 mm. (0.015 inch) thick, and the reverse side was then used, the celluloid being backed by white card. A sample prepared for the purpose showed that the ink so viewed through the thickness of the material had a reflectionfactor 0.73 of that of the adjacent uninked celluloid backed by the white card. The contrast in this case was therefore 100:

73. Three sizes of test-object of this contrast were used, the scale-units being 2, 3 and 4 mm. respectively (4). These proved in the outcome to correspond, as to visibility, with the three high contrast test-objects, each to each, described under

I.

The test-object was seen binocularly by the subject, who was seated in an unlighted room, through a rectangular wallopening 41 by 51 cm at 3 meters' distance. The screen bearing the test-object was 6 meters from the subject. It was more than large enough to fill the wall-opening from the subject's location. No auxiliary fixation-point was used, the eyes being fixated directly upon the area of the test-object.

The screen was lighted by a set of interchangeable systems similar to those previously described (1, 2). With the maximal voltage used (110 volts) the various sets of lamps yielded a series of brightnesses varying by a factor of about 2. In order to get smaller intervals than this for the serial steps, reduced voltages were used on the various sets of lamps, the maximum being 110 (on lamps rated at 115) and the lowest used being 86. The entire brightness range was (in sect. I.) from 141 to 0.021 ml. and (in sect. II.) from 131 to 0.013 ml. By selecting the reduced voltages these ranges were divided into steps forming approximate geometric series, the ratios being unavoidably somewhat unequal and of the order of I: 1.37 or 0.73 I.

From about 5 ml. down, instead of a pair of lamps at the level of the test-object and somewhat laterally placed on either side, a single lamp was used, placed in the median plane of the apparatus. From about 4 to 0.4 ml. the lamp was hung above the visual line near the partition; and for brightnesses below this the lamp was placed below the visual line, enclosed in a box near the floor. The box was provided with a diffusing light of milk-flashed glass, stopped down as necessary with calibrated cardboard diaphragms. The voltage control for the serial steps was used for the single lamps as for the pairs.

The arrangement of light sources above and below the visual line was objectionable, since this caused one of the horizontal borders of the mask-opening to cast a shadow on the card.

bearing the test object. Although readily visible, this shadow was little in evidence on the confusion-patterns owing to their close proximity to the mask; while in the case of the testobject the shadow encroached upon the card only, leaving the test-object fully illuminated as well as a substantial interval on the blank cardboard.

RESULTS

In Section I. of the work (contrast of test-object 100: 4), thirty-two subjects participated; in Section II. (contrast 100 73), thirty. Owing to individual differences some of these failed to yield threshold-values for the more difficult conditions; i.e., for the smaller test objects and for the shorter times. To furnish an estimate of these individual variations, as well as to gain an idea apart from them as to the reliability of the mean results, Table I. was prepared. This includes only those conditions within which every subject (less one, in one case, each section) yielded a threshold-value.

The values given under the column-headings T, 2000, 1000 and 500 are the mean logarithms of the brightness in millilamberts for threshold vision of the test-object indicated within the time specified. In each case the number in parentheses is the number of results yielding the average, and the value just below is the standard deviation of the single measurement. In the columns and rows headed "dif." are similarly given the average differences between the log's. brightness for the conditions adjacent in the table. These differences were computed for the individual cases, and their standard deviations (a in the table) computed independently.

The measure of precision of a sum or difference is the quadratic sum (square root of the sum of the squares) of the similar measures of the two quantities. On the tentative assumption that all of the variabilities are accidental, the corresponding standard deviations of the differences between the mean log's. have been computed and entered (b) below the standard deviations of the mean differences (a). From the fact that b is always larger than a, by a factor of 2 or more, we may draw the conclusion that the differences in the log's. brightness as between any two conditions are less subject to