TABLE I

MEAN THRESholds, StateD AS LOG. BRIGHTNESS, and DifferencES FOR COMPLETE GROUPS OF (Sect. I.) 32 AND (Sect. II.) 30 INDIVIDUALS

Below each mean log. is given its standard deviation. For the differences these were computed (a) directly from the separate differences
between the log's. brightness for the individuals and, (b) as the square root of the sum of the squares of the standard deviations of the two
mean logs. The fact that the latter (b) are always the larger indicates that the individual variations are predominantly in the absolute
brightness rather than in the differences between one brightness and another. The former (a) are made use of in the text to appraise the
reliability of the experimental method.

The number in parentheses is, in each case, the number of terms involved in the average. This is the whole number of subjects in the
group, except for one case in each section.

individual variation than the log's. brightness themselves. This was perhaps to be expected; for presumably under any two conditions as to the test-stimulus, the threshold brightnesses will both be higher or both lower for one individual than for another, according as he required more or less light for an equal result. While it cannot be assumed that the difference is in any particular case free from individual variation, it is still conservative to use the differences rather than the brightnesses themselves as a basis for a measure of the reliability of the experimental method.

From Section I. it appears that the mean of the three standard deviations of the differences is 0.34. The standard deviation of one of the terms, assuming both to have the same. reliability, would be times this or 0.24. Since we are dealing with common logarithms here, the limits corresponding to (mean log.) 0.24 will be numerically as 1.74 and 0.58, where the geometric mean brightness is as unity.

From Section II. (Table I.) the mean standard deviation of the difference is 0.21, the standard deviation of log. brightness computed therefrom is 0.14, corresponding similarly to 1.38 and 0.73 of the mean brightness.

In Fig. 2 are plotted the common logarithms of the threshold brightness for each size of test-object and for each time of exposure, both for the high and for the low contrast test-objects. The reciprocal of the time appears as ordinate and log. brightness as abscissa. Fig. 2A gives the actual average log. brightness obtained from ten subjects who gave complete results except, at least, for the smallest object and for the shortest time (500). This value for the group was supplied by taking the mean difference between the values of log. brightness for 500 and 1000 for the same test-object and for the subjects who yielded the necessary results; and adding this difference to the mean log. brightness at 1000 for all subjects in the group A. The difference so added and the number of subjects from whom it was derived are indicated in Table IIA.

Fig. 2B shows the results similarly reconstructed for the entire group of 21 subjects who happened to be available for

both sections of the work, and Table IIB. shows, similarly, how far the results are the actual average results, as well as the basis and the procedure of reconstruction of the missing values.

TABLE II

THE GEOMETRIC MEAN THRESHOLDS, EXPRESSED AS LOG. BRIGHTNESS,

FOR ALL CONDITIONS

4. Ten subjects who yielded values at all conditions except as indicated for 500 exposure time, smallest object.

B. Twenty-one subjects, values reconstructed where results are incomplete, as indicated.

DISCUSSION

It is to be remembered that the ordinates of Fig. 2 are the reciprocals of the threshold times ('speeds'). Plotting the actual times would be embarrassing in those cases (T) where the time was ad libitum. As a matter of fact, the responses in these cases appeared to casual observation little, if at all, less

FIG. 2. The brightness of test-object ground required for 50 per cent. correct responses with various times of exposure.

The ordinates are 'speeds' (reciprocal threshold times), assumed to be equal to I for ad libitum exposure. Abscissæ are plotted as log. brightness, millilamberts. Solid lines and dots indicate contrast 100: 4, the test object and confusion patterns being drawn with india ink on white card. Broken lines and circles, contrast 100: 73 patterns drawn on celluloid and reversed (see text).

A. Ten subjects, selected: B. Twenty-one subjects, unselected.

prompt than when the time was limited by the falling of the second drop. In other instances there was more hesitancy, sometimes to the extent of several seconds; although this happened now and again when the exposure time was limited.

It would be difficult to indicate upon a plot the fact that a value was somewhere between, say, 200 and infinity. By plotting 'speeds,' on the other hand, it is possible to indicate the results. In the figure the results for the ad libitum exposure have been plotted as if the time averaged I second ('speed' unity); and the curves have been drawn toward, but not to, this point. This fact must be remembered in the study of Fig. 2.

=

Inspection of the figure shows that in general the relation between 'speed' and log. brightness is not far from linear. A straight line on the plot would indicate that each multiplication of the brightness by a constant factor afforded an equal increase in 'speed.' But not only do the lines in the plot show a slight curvature, with the concavity upward, but the curves for the different test-objects show in general different slopes for the same time differences; in the sense that the smaller test objects require a larger factor of increase in brightness than the larger (5). The same is true when the contrast becomes smaller, comparing, for example, the two curves for the 2 mm. test-object (Fig. 2A). In fact it appears to be true that reducing the contrast from 100 : 4 to 100: 73 (that is, from white and black to white and gray) is almost exactly equivalent to reducing the size of the test-object by one step in the series 4, 3, 2, 1. On the other hand, when the test-object is made more difficult by decreasing the time of exposure, it would appear from the curvature of the lines in the figure that successive increments in "speed" thereby made necessary are accomplished with the help of light increased by successively smaller factors.

Some of the conclusions just stated will perhaps appear more definitely from a study of Fig. 3. Aa and Ba show the relations found between the dimensions of the testobjects and log. brightness, for the various exposure-times and for both contrasts. In so far as the comparison is possible, the curves indicate that ad libitum exposure with the low contrast is equivalent to something between 100 and 2000 with the high; and that 2000 with the low is equivalent to slightly more than 500 with the high. In the latter case