THE VARIABILITY OF INTENSITY DISCRIMINATION BY THE HONEY BEE IN RELATION TO VISUAL ACUITY

Variation in the determined magnitudes of the difference in brightness between alternating members of a system of stripes requisite for the elicitation of a threshold response in bees shows that the intensity of excitation, as a function of width of stripe and of intensity of illumination, is determined by the intensity of illumination and by the frequency of occurrence of divisions between bright and less bright bars. The variation of ΔI is limited by the intensity of excitation, so that the curves relating P.E. (ΔI/I) have the same form in relation to I as do the curves for ΔI/I. The limiting rule according to which P.E. ΔI is a power function of I for stripes of maximum usable width is departed from more and more markedly, for lower intensities, as narrower stripes are employed.     

THE VISUAL INTENSITY DISCRIMINATION OF THE HONEY BEE

1. Bees respond by a characteristic reflex to a movement in their visual field. By confining the field to a series of parallel stripes of different brightness it is possible to determine at any brightness of one of the two stripe systems the brightness of the second at which the bee will first respond to a displacement of the field. Thus intensity discrimination can be determined. 2. The discriminating power of the bee''s eye varies with illumination in much the same way that it does for the human eye. The discrimination is poor at low illumination; as the intensity of illumination increases the discrimination increases and seems to reach a constant level at high illuminations. 3. The probable error of See PDF for Equation decreases with increasing I exactly in the same way as does See PDF for Equation itself. The logarithm of the probable error of ΔI is a rectilinear function of log I for all but the very lowest intensities. Such relationships show that the measurements exhibit an internal self-consistency which is beyond accident. 4. A comparison of the efficiency of the bee''s eye with that of the human eye shows that the range over which the human eye can perceive and discriminate different brightnesses is very much greater than for the bee''s eye. When the discrimination power of the human eye has reached almost a constant maximal level the bee''s discrimination is still very poor, and at an illumination where as well the discrimination power of the human eye and the bee''s eye are at their best, the intensity discrimination of the bee is twenty times worse than in the human eye.     

ON THE RELATION BETWEEN MEASUREMENTS OF INTENSITY DISCRIMINATION AND OF VISUAL ACUITY IN THE HONEY BEE

1. Bees respond by a characteristic reflex to a movement of their visual field. By confining the field to a series of parallel stripes of two alternating different brightnesses it is possible to determine for any width of stripe, at any brightness of one of the two sets of stripes, the brightness of the second at which the bee will first respond to a displacement of the field. Thus the relations between visual acuity and intensity discrimination can be studied. 2. For each width of stripe and visual angle subtended by the stripe the discrimination power of the bee''s eye for different brightnesses was studied. For each visual acuity the intensity discrimination varies with illumination in a characteristic, consistent manner. The discrimination is poor at low illuminations; as the intensity of illumination increases the discrimination increases, and reaches a constant level at high illuminations. 3. From the intensity discrimination curves obtained at different visual acuities, visual acuity curves can be reconstructed for different values of ΔI/I. The curves thus obtained are identical in form with the curve found previously by direct test for the relation between visual acuity and illumination.     

ON THE VARIABILITY OF CRITICAL ILLUMINATION FOR FLICKER FUSION AND INTENSITY DISCRIMINATION

From the data of experiments with bees in which threshold response is employed as a means of recognizing visual discrimination between stripes of equal width alternately illuminated by intensities I ₁ and I ₂, it is shown that the detectable increment of intensity ΔI, where ΔI = I ₂ - I ₁, is directly proportional to σ_I2 (I ₁ being fixed). From tests of visual acuity, where I ₁ = 0 and the width of the stripes is varied, σ_I2 = kI ₂ + const.; here I ₂ = ΔI, and ΔI/I ₂ = 1. When the visual excitability of the bee is changed by dark adaptation, λI ≡ kΔI (= k'' σ_ΔI) = k'''' I + const. For the measurements of critical illumination at threshold response to flicker, σ_I2 (= σ_ΔI) = k I ₂ = k'' ΔI + const. The data for critical illumination producing threshold response to flicker in the sun-fish Lepomis show for the rods σ_I2 = K I ₂ for the cones σ_I2 = K''(I ₂ + const.). The data thus indicate that in all these experiments essentially the same visual function is being examined, and that the recognition of the production of a difference in effect by alternately illuminated stripes takes place in such a way that d (ΔI)/d (σ_I2) = const., and that ΔI is directly proportional to I (or "I ₂," depending on the nature of the experiment). It is pointed out that the curve for each of the cases considered can be gotten equally well if mean I or σ_I is plotted as a function of the independent variable involved in the experiment. Certain consequences of these and related facts are important for the treatment of the general problem of intensity discrimination.     

A THEORY OF VISUAL INTENSITY DISCRIMINATION

1. A theory of visual intensity discrimination is proposed in terms of the photochemical events which take place at the moment when a photosensory system already adapted to the intensity I is exposed to the just perceptibly higher intensity I+ΔI. Unlike previous formulations this theory predicts that the fraction ΔI/I, after rapidly decreasing as I increases, does not increase again at high intensities, but reaches a constant value which is maintained even at the highest intensities. 2. The theory describes quantitatively the intensity discrimination data of Drosophila, of the bee, and of Mya. 3. With some carefully considered exceptions the intensity discrimination data of the human eye fall into two classes: those with small test areas or with red light, which form a single continuous curve describing the function of the retinal cones alone, and those with larger areas, and with white, orange, and yellow light, which form a double curve showing a clear inflection point, and represent the separate function of the rods at intensities below the inflection point and of the cones at intensities above it. 4. The theory describes all these data quantitatively by treating the rods and cones as two independently functioning photosensory systems in accordance with the well established duplicity idea. 5. In terms of the theory the data of intensity discrimination give critical information about the order of both the photochemical and dark reactions in each photosensory system. The reactions turn out to be variously monomolecular and bimolecular for the different animals.     

INTENSITY DISCRIMINATION IN THE HUMAN EYE : I. THE RELATION OFΔI/ITO INTENSITY

New measurements of the brightness difference sensibility of the eye corroborate the data of previous workers which show that ΔI/I decreases as I increases. Contrary to previous report, ΔI/I does not normally increase again at high intensities, but instead decreases steadily, approaching a finite limiting value, which depends on the area of the test-field and on the brightness of the surrounding field. On a logarithmic plot, the data of ΔI/I against I for test-fields below 2° are continuous, whereas those for test-fields above 2° show a sharp discontinuity in the region of intensity in which ΔI/I decreases rapidly. This discontinuity is shown to divide the data into predominantly rod function at low intensities, and predominantly cone function at high intensities. Fields below 2° give higher values of ΔI/I at all intensities, when compared with larger fields. Fields greater than one or two degrees differ from one another principally on the low intensity side of the break. Changes in area above this limit are therefore mainly effective by changing the number of rods concerned. This is confirmed by experiments controlling the relative numbers of rods and cones with lights of different wavelength and with different retinal locations. At high intensities ΔI/I is extremely sensitive to changes in brightness of surrounding visual fields, except for large test-fields which effectually furnish their own surrounds. This sensitivity is especially marked for fields of less than half a degree in diameter. Although the effect is most conspicuous for high intensities, the surround brightness seems to affect the relation between variables as a whole, except in very small fields where absence of a surround of adequate brightness results in the distortion of the theoretical relation otherwise found. The theoretical relationship for intensity discrimination derived by Hecht is shown to fit practically all of the data. Changes in experimental variables such as retinal image area, wavelength, fixation, and criterion may be described as affecting the numerical quantities of this relationship.     

INTENSITY DISCRIMINATION IN THE HUMAN EYE : II. THE RELATION BETWEENΔI/IAND INTENSITY FOR DIFFERENT PARTS OF THE SPECTRUM

1. A new apparatus is described for measuring visual intensity discrimination over a large range of intensities, with white light and with selected portions of the spectrum. With it measurements were made of the intensity ΔI which is just perceptible when it is added for a short time to a portion of a field of intensity I to which the eye has been adapted. 2. For white and for all colors the fraction ΔI/I decreases as I increases and reaches an asymptotic minimum value at high values of I. In addition, with white light the relation between ΔI/I and I shows two sections, one at low intensities and the other at high intensities, the two being separated by an abrupt transition. These findings are contrary to the generally accepted measurements of Koenig and Brodhun; however, they confirm the recent work of Steinhardt, as well as the older work of Blanchard and of Aubert. The abrupt transition is in keeping with the Duplicity theory which attributes the two sections to the functions of the rods and cones respectively. 3. Measurements with five parts of the spectrum amplify these relationships in terms of the different spectral sensibilities of the rods and cones. With extreme red light the relation of ΔI/I to I shows only a high intensity section corresponding to cone function, while with other colors the low intensity rod section appears and increases in extent as the light used moves toward the violet end of the spectrum. 4. Like most of the previously published data from various sources, the present numerical data are all described with precision by the theory which supposes that intensity discrimination is determined by the initial photochemical and chemical events in the rods and cones.     

THE VISUAL DISCRIMINATION OF INTENSITY AND THE WEBER-FECHNER LAW

1. A study of the historical development of the Weber-Fechner law shows that it fails to describe intensity perception; first, because it is based on observations which do not record intensity discrimination accurately, and second, because it omits the essentially discontinuous nature of the recognition of intensity differences. 2. There is presented a series of data, assembled from various sources, which proves that in the visual discrimination of intensity the threshold difference ΔI bears no constant relation to the intensity I. The evidence shows unequivocally that as the intensity rises, the ratio See PDF for Equation first decreases and then increases. 3. The data are then subjected to analysis in terms of a photochemical system already proposed for the visual activity of the rods and cones. It is found that for the retinal elements to discriminate between one intensity and the next perceptible one, the transition from one to the other must involve the decomposition of a constant amount of photosensitive material. 4. The magnitude of this unitary increment in the quantity of photochemical action is greater for the rods than for the cones. Therefore, below a certain critical illumination—the cone threshold—intensity discrimination is controlled by the rods alone, but above this point it is determined by the cones alone. 5. The unitary increments in retinal photochemical action may be interpreted as being recorded by each rod and cone; or as conditioning the variability of the retinal cells so that each increment involves a constant increase in the number of active elements; or as a combination of the two interpretations. 6. Comparison with critical data of such diverse nature as dark adaptation, absolute thresholds, and visual acuity shows that the analysis is consistent with well established facts of vision.     

THEORY AND MEASUREMENT OF VISUAL MECHANISMS : III. ΔI AS A FUNCTION OF AREA,INTENSITY, AND WAVE-LENGTH,FOR MONOCULAR AND BINOCULAR STIMULATION

Measurements of ΔI as a function of retinal area illuminated have been obtained at various levels of standard intensity I ₁, using "white" light and light of three modal wave-lengths (λ465, 525, 680), for monocular stimulation and for simultaneous excitation of the two eyes ("binocular"), using several methods of varying (rectangular) area and retinal location, with control of exposure time. For data homogeneous with respect to method of presentation, log ΔI_m = -Z log A + C, where ΔI = Ĩ ₂ – I ₁, A is area illuminated, and C is a terminal constant (= log ΔI_m for A = 1 unit) depending on the units in which ΔI and A are expressed, and upon I ₁. The equation is readily deduced on dimensional grounds, without reference to specific theories of the nature of ΔI or of retinal area in terms of its excitable units. Z is independent of the units of I and A. Experimentally it is found to be the same for monocular and binocular excitations, as is to be expected. Also as is expected it is not independent of λ, and it is markedly influenced by the scheme according to which A is varied; it depends directly upon the rate at which potentially excitable elements are added when A is made to increase. For simultaneous excitation of the two eyes (when of very nearly equivalent excitability), ΔĪ_B is less than for stimulation of either eye alone, at all levels of I ₁, A, λ. The mean ratio (ΔĪ_L + ΔĪ_R)/2 to ΔI^B was 1.38. For white light, doubling A on one retina reduces ΔI_m in the ratio 1.21, or a little less than for binocular presentation under the same conditions. These facts are consistent with the view that the properties of ΔI are quantitatively determined by events central to the retina. The measure σ_1ΔI of organic variation in discrimination of intensities and ΔI_m are found to be in simple proportion, independent of I ₁, A, λ (and exposure time). Variability (σ_1ΔI) is not a function of the mode of presentation, save that it may be slightly higher when both retinas are excited, and its magnitude (for a given level of ΔI_m) is independent of the law according to which the adjustable intensity I ₂ is instrumentally controlled.     

ANOXIA AND BRIGHTNESS DISCRIMINATION

1. Brightness discrimination has been studied with individuals breathing oxygen concentrations corresponding to 7 altitudes between sea level and 17,000 feet. The brightnesses were 0.1, 0.01, and 0.001 millilambert involving only daylight (cone) vision. 2. At these light intensities, brightness discrimination begins to deteriorate at fairly low altitudes. The deterioration is obvious at 8,000 feet, and becomes marked at 15,000 feet, where at low brightness, the contrast must be increased 100 per cent over the sea level value before it can be recognized. 3. The impairment of brightness discrimination with increase in altitude is greater at higher altitudes than at lower. The impairment starts slowly and becomes increasingly rapid the higher the altitude. 4. Impairment of brightness discrimination varies inversely with the light intensity. It is most evident under the lowest light intensities studied, but shows in all of them. However, it decreases in such a way that the deterioration is negligible in full daylight and sunlight. 5. The thresholds of night (rod) vision and day (cone) vision are equally affected by anoxia. 6. The quantitative form of the relation between brightness discrimination ΔI/I and the prevailing brightness I remains the same at all oxygen concentrations. The curve merely shifts along the log I axis, and the extent of the shift indicates the visual deterioration. 7. The data are described in terms of retinal chemistry. Since anoxia causes only a shift in log I it is shown that the photochemical receptor system cannot be affected. Instead the conversion of photochemical change into visual function is impaired in such a way that the conversion factor varies as the fourth power of the arterial oxygen saturation.     

THE EFFECTS OF ULTRAVIOLET RADIATION ON SPORES OF THE FUNGUS ASPERGILLUS NIGER

The survival ratio of Aspergillus spores exposed to ultraviolet radiation has been measured as a function of total incident energy for wave lengths of 2537 Å, 3022 Å, 3129 Å, and 3650 Å. The effect of humidity on killing of Aspergillus spores by ultraviolet radiation has been found to be negligible. A delay in germination as a result of irradiation has been found. The Bunsen-Roscoe reciprocity law has been found to hold within the limits of the radiation intensities studied. Certain morphological changes have been observed.     

THEORY AND MEASUREMENT OF VISUAL MECHANISMS : I. A VISUAL DISCRIMINOMETER. II. THRESHOLD STIMULUS INTENSITY AND RETINAL POSITION

Monocular threshold stimulus intensities (ΔI_o, photons) were measured along the 0–180° meridian of human retinae for three observers. The test image was small (= 0.08°) and of short duration (= 0.20 second). ΔI_o was found to decrease as the angular distance from the fovea was increased. Actual counts of the number of retinal elements per mm.² along the 0–180° meridian (Østerberg) were compared with the obtained results. No direct correlation was found to exist between visual sensitivity and the number of retinal elements. Binocular threshold stimuli were also measured along the same meridian. The form of the function relating binocular visual sensitivity and retinal position was discovered to be essentially similar to that for monocular sensitivity, but is more symmetrical about the center of the fovea. The magnitude of the binocular measurement is in each case smaller than that of the monocular threshold stimulus intensity for the more sensitive eye. The ratio is statistically equal to 1.4 (a fact which suggests Piper''s rule). These results are shown to be consistent with the hypothesis that the process critical for the eventuation of the threshold response is localized in the central nervous system. They are not consistent with the view that the quantitative properties of visual data are directly determined by properties of the peripheral retina.     

THE VISUAL ACUITY AND INTENSITY DISCRIMINATION OF DROSOPHILA

Drosophila possesses an inherited reflex response to a moving visual pattern which can be used to measure its capacity for intensity discrimination and its visual acuity at different illuminations. It is found that these two properties of vision run approximately parallel courses as functions of the prevailing intensity. Visual acuity varies with the logarithm of the intensity in much the same sigmoid way as in man, the bee, and the fiddler crab. The resolving power is very poor at low illuminations and increases at high illuminations. The maximum visual acuity is 0.0018, which is 1/1000 of the maximum of the human eye and 1/10 that of the bee. The intensity discrimination of Drosophila is also extremely poor, even at its best. At low illuminations for two intensities to be recognized as different, the higher must be nearly 100 times the lower. This ratio decreases as the intensity increases, and reaches a minimum of 2.5 which is maintained at the highest intensities. The minimum value of ΔI/I for Drosophila is 1.5, which is to be compared with 0.25 for the bee and 0.006 for man. An explanation of the variation of visual acuity with illumination is given in terms of the variation in number of elements functional in the retinal mosaic at different intensities, this being dependent on the general statistical distribution of thresholds in the ommatidial population. Visual acuity is thus determined by the integral form of this distribution and corresponds to the total number of elements functional. The idea that intensity discrimination is determined by the differential form of this distribution—that is, that it depends on the rate of entrance of functional elements with intensity—is shown to be untenable in the light of the correspondence of the two visual functions. It is suggested that, like visual acuity, intensity discrimination may also have to be considered as a function of the total number of elements active at a given intensity.     

The effect of varying the intensity and the duration of preexposure upon foveal dark adaptation in the human eye

The course of foveal dark adaptation was studied as a function of the intensity and duration of preexposure. Four intensities (11,300, 5,650, 1,130, and 565 mL.) and four durations (300, 150, 30, and 15 seconds) were used in all combinations of intensity and duration. The threshold-measuring instrument was a monocular Hecht-Shlaer adaptometer and the threshold measurements were recorded in log micromicrolamberts. There were two subjects and each went through the complete series of intensities and durations five times. The five logarithmic values obtained for each threshold were converted into a geometric mean and these means were the data used in the analysis of the results. The chief results were as follows:— 1. For each subject the final steady threshold value was in the region of 7.0 log µµL. 2. As the intensity, or duration, or both, were increased the initial foveal dark adaptation threshold rose, the slope of the curve decreased, and the time to reach a final steady threshold value increased. 3. For those values of preexposure intensity and time for which the product, I x t, is a constant it was found that for the two higher intensities and two longer durations and also for the two lower intensities and two shorter durations, the dark adaptation curves were the same. For other values of I x t = C the curves were generally not the same.     

THE PHOTOCHEMICAL NATURE OF THE PHOTOSENSORY PROCESS

1. In order to produce a response in Mya, the minimum amount of light energy required is 5.62 meter candle seconds. This energy follows the Bunsen-Roscoe law for the relation between intensity and time of exposure. 2. The necessary minimum amount of energy varies but little with the temperature; the temperature coefficient for 10°C. is 1.06. 3. In view of these facts it is concluded that the initial action of the light is photochemical in nature. This substantiates the hypothesis previously suggested to account for the mechanism of photoreception. 4. The constant energy requirement for stimulation of Mya shows that the traditional division of animals into those which respond to a constant source of light and those which respond to a rapidly augmented light is without any fundamental significance for sensory physiology.     

THE ORIENTATION OF ANIMALS BY OPPOSED BEAMS OF LIGHT

When orientation is attained under the influence of beams of parallel light opposed at 180° the deflection θ from a path at right angles to the beams is given by tan See PDF for Equation, where I ₁ and I ₂ are the photic intensities and H is the average angle between the photoreceptive surfaces. This expression is independent of the units in which I is measured, and holds whether the primary photosensory effect is proportional to I or to log I. When photokinetic side-to-side motions of the head occur, H decreases with increasing total acting light intensity, but increases if higher total light intensity restricts the amplitude of random movements; in each case, H is very nearly proportional to log I ₁ I ₂. For beams of light at 90°, See PDF for Equation. The application of these equations to some particular instances is discussed, and it is shown why certain simpler empirical formulæ previously found by others yield fair concordance with the experimental data. The result is thus in complete accord with the tropism theory, since the equations are based simply on the assumption that when orientation is attained photic excitation is the same on the two sides.     

ON THE GEOTROPIC ORIENTATION OF HELIX

The snail Helix nemoralis in negatively geotropic creeping orients upward upon an inclined surface until the angle of the path of progression (θ) is related to the tilt of the surface (α) as (Δ sin θ) (Δ sin α) = – const.; θ is very nearly a rectilinear function of log sin α. The precision of orientation (P.E._θ) declines in proportion to increasing sin α, P.E._θ/^θ in proportion to θ. These facts are comprehensible only in terms of the view that the limitation of orientation is controlled by the sensorial equivalence of impressed tensions in the anterior musculature.     

THE PHOTOCHEMICAL BASIS OF ANIMAL HELIOTROPISM

1. Experiments on the heliotropic orientation of Limulus were made which confirmed Loeb''s photochemical theory of animal heliotropism proposed first in 1888 and 1889 in experiments on insects, and later in experiments on other forms of animals. 2. It is shown that these animals are oriented by light in such a way that the product I x t x cos α is the same for the symmetrical photosensitive elements of the eyes or the skin, where I is the intensity of the light, t the duration of illumination, and α the angle of incidence of the light at the surface element of the photosensitive organ. 3. When this equation holds, the products of decomposition by light must be the same in symmetrical elements of the eyes or skin, and the influence of these products of decomposition on the tension of symmetrical muscles of the locomotor organs of the animal must be the same. As a consequence the animal must move in the path of light, either to or from the source of light.     

ON THE EQUILIBRATION OF GEOTROPIC AND PHOTOTROPIC EXCITATIONS IN THE RAT

The intensity of light required to just counterbalance geotropic orientation of young rats, with eyelids unopened, is so related to the angle of inclination (α) of the creeping plane that the ratio log I/log sin α is constant. This relationship, and the statistical variability of I as measured at each value of α, may be deduced from the known phototropic and the geotropic conduct as studied separately, and affords proof that in the compounding of the two kinds of excitation the rat is behaving as a machine.