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.     

Primary Events, Energy Transfer, and Reactions in Photosynthetic Events: Lifetime of the Excited State In Vivo: II. Bacteriochlorophyll in Photosynthetic Bacteria at Room Temperature

Lifetime of the excited state (τ) of bacteriochlorophyll (BChl) in photosynthetic bacteria, measured with a mode-locked argon laser (oscillating at 488 nm; mode locked at 56 MHz) as light source, ranged from 0.3 to 2.5 nsec. These τ values are reported with a precision of ±0.1 nsec. The value of τ at high exciting light intensity (I) was two to three times that at low intensity. For young cultures of green bacterium Chloropseudomonas ethylicum, τ ranged from 0.5 (low I) to 1.0 nsec (high I); for those of the purple bacterium Rhodospirillum rubrum, from 0.4 (low I) to 1.0 nsec (high I); and for those of the BChl b-containing Rhodopseudomonas viridis, from 1.0 (low I) to 2.5 nsec (high I). These data provide information regarding the efficiencies of the photochemical process in these bacteria. Quantum yield (ø) of BChl fluorescence, calculated from ø = τ/τ₀ (where τ₀ is the intrinsic lifetime of fluorescence), ranges from 2-6% at low intensities to 6-14% at high intensities.     

CRITICAL ILLUMINATION AND FLICKER FREQUENCY,AS A FUNCTION OF FLASH DURATION: FOR THE SUNFISH

From the relations between critical illumination in a flash (I_m) and the flash frequency (F) for response of the sunfish to visual flicker when the proportion of light time to dark time (t_L/t_D) in a flicker cycle is varied at one temperature (21.5°) the following results are obtained: At values of t_L/t_D between 1/9 and 9/1 the F - log I_m curves are progressively shifted toward higher intensities and lower F_max.. F_max. is a declining rectilinear function of the percentage of the flash cycle time occupied by light. The rod and the cone portions of the flicker curve are not shifted to the same extent. The cone portion and the rod region of the curve are each well described by a probability integral. In terms of F as 100 F/F_max. the standard deviation of the underlying frequency distribution of elemental contributions, summed to produce the effect proportional to F, is independent of t_L/t_D. The magnitude of log I_m at the inflection point (r''), however, increases rectilinearly with the percentage light time in the cycle. The proportionality between I_m and σ_II1 is independent of t_L/t_D. These effects are interpreted as consequences of the fact that the number of elements of excitation available for discrimination of flicker is increased by increasing the dark interval in a flash cycle. Decreasing the dark interval has therefore the same kind of effect as reducing the visual area, and not that produced by decreasing the temperature.     

TEMPERATURE AND CRITICAL ILLUMINATION FOR REACTION TO FLICKERING LIGHT : I. ANAX LARVAE

The curve of mean critical illumination (I_m) for response to flicker as a function of flicker frequency (F) for the larvae of the dragonfly Anax junius is progressively shifted toward higher intensities the lower the temperature. The maximum flicker frequency (one half the cycle time of light and no light) and the maximum intensity with which it is associated are very little if at all affected by change of temperature. These facts are in agreement with the requirements of the conception that recognition of critical illumination for reaction to flicker involves and depends upon a kind of intensity discrimination, namely between the effects of flashes and the after effects of these flashes during the intervals of no light. The shift of the F-I_m curve with change of temperature is quite inconsistent with the stationary state conception of the determination of the shape of the curve. The dispersion (P.E. _II1) of the measurements of I ₁ is directly proportional to I_m, but the factor of proportionality is less at high and at low temperature than at an intermediate temperature; the scatter of the values of P.E. _II1 is also a function of the temperature. These facts can also be shown to be concordant with the intensity discrimination basis for marginal recognition of flicker.     

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.     

TEMPERATURE AND CRITICAL ILLUMINATION FOR REACTION TO FLICKERING LIGHT : IV. ANAX NYMPHS

At fixed flash frequency (_F = 20, _F = 55) and with constant light time fraction (50 per cent) in the flash cycle, the critical illumination I for response of Anax nymphs to visual flicker falls continuously as the temperature rises. The temperature characteristic µ for the measure of excitability (1/I) increases continuously with elevation of temperature. The form of the F - log I curve does not change except at quite high temperature (35.8°), and then only slightly (near F = 55); F_max. is not altered. The very unusual form of the 1/I curve as a function of temperature is quantitatively accounted for if two processes, with respectively µ = 19,200 and µ = 3,400, contribute independently and simultaneously to the control of the speed of the reaction governing the excitability; the velocities of these two processes are equal at 15.9°.     

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.     

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.     

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.     

TEMPERATURE AND CRITICAL ILLUMINATION FOR REACTION TO FLICKERING LIGHT : II. SUNFISH

The curve connecting mean critical illumination (I_m) and flicker frequency (F) for response of the sunfish Lepomis (Enneacanthus gloriosus) to flicker is systematically displaced toward lower intensities by raising the temperature. The rod and cone portions of the curve are affected in a similar way, so that (until maximum F is approached) the shift is a nearly constant fraction of I_m for a given change of temperature. These relationships are precisely similar to those found in the larvae of the dragonfly Anax. The modifications of the variability functions are also completely analogous. The effects found are consistent with the view that response to flicker is basically a matter of discrimination between effect of flashes of light and their after effects,—a form of intensity discrimination. They are not consistent with the stationary state formulation of the shape of the flicker curve. An examination of the relationships between the cone portion and the rod portion of the curves for the sunfish suggests a basis for their separation, and provides an explanation for certain "anomalous" features of human flicker curves. It is pointed out how tests of this matter will be made.     

INTERMITTENT STIMULATION BY LIGHT : III. THE RELATION BETWEEN INTENSITY AND CRITICAL FUSION FREQUENCY FOR DIFFERENT RETINAL LOCATIONS

When measurements of the critical fusion frequency for white light over a large range of intensities are made with the rod-free area of the fovea, the relation between critical frequency and log I is given by a single sigmoid curve, the middle portion of which approximates a straight line whose slope is 11.0. This single relation must be a function of the foveal cones. When the measurements are made with a retinal area placed 5° from the fovea, and therefore containing both rods and cones, the relation between critical frequency and log I shows two clearly separated sections. At the lower intensities the relation is sigmoid and reaches an upper level at about 10 cycles per second, which is maintained for 1.25 log units, and is followed by another sigmoid relationship at the higher intensities similar to the one given by the rod-free area alone. These two parts of the data are obviously separate functions of the rods at low intensities and of the cones at high intensities. This is further borne out by similar measurements made with retinal areas 15° and 20° from the fovea where the ratio of rods to cones is anatomically greater than at 5°. The two sections of the data come out farther apart on the intensity scale, the rod portion being at lower intensities and the cone portion at higher intensities than at 5°. The general form of the relation between critical frequency and intensity is therefore determined by the relative predominance of the cones and the rods in the retinal area used for the measurements.     

TEMPERATURE AND CRITICAL ILLUMINATION FOR REACTION TO FLICKERING LIGHT : V. XIPHOPHORUS,PLATYPOECILIUS, AND THEIR HYBRIDS

For the teleosts Xiphophorus montezuma, Platypoecilius maculatus, and their F ₁ hybrids the temperature characteristics (µ in Arrhenius'' equation) are the same for the shift of the low intensity and the high intensity segments of the respective and different flicker response contours (critical intensity I as a function of flash frequency F, with light time fraction constant, at 50 per cent). The value of µ is 12,500 calories or a very little less, over the range 12.5 to 36°. This shows that 1/I can be understood as a measure of excitability, with F fixed, and that the excitability is governed by the velocity of a chemical process common to both the classes of elements represented in the duplex performance curve (rods and cones). It is accordingly illegitimate to assume that the different shapes of the rod and cone branches of the curves are determined by differences in the chemical mechanisms of excitability. It is also forbidden to assume that the differing form constants for the homologous segments in the curves for two forms (X. and P.) are the reflections of a difference in the chemical factors of primary excitability. These differences are determined by statistical factors of the distribution of excitabilities among the elements implicated in the sensory effect vs. intensity function, and are independent of temperature and of the temperature characteristic. It must be concluded that the physicochemical nature of the excitatory process cannot be deduced from the shape of the performance contour. The form constants (σ''_{log I} and F_max.) for F vs. log I are specifically heritable in F ₁, although µ is here the same as for X. and P. In an intergeneric cross one cannot in general expect Mendelian simplicity of segregation in subsequent generations, and in the present case we find that F ₂ individuals are indistinguishable from F ₁, both as regards F vs. log I and as regards the variation of I within a group of 17 individuals. The result in F ₂ definitely shows, however, that certain specific statistical form constants for the F-log I contour are transmissible in inheritance. It is pointed out that there thus is provided an instance in which statistical (distribution) factors in performance characteristics involving the summating properties of assemblages of cellular units are heritable in a simple manner without the implication of detectable differences in chemical organization of the units involved. This has an important bearing upon the logic of the theory of the gene.     

BRIGHTNESS DISCRIMINATION AS A FUNCTION OF THE DURATION OF THE INCREMENT IN INTENSITY

1. This investigation has been concerned with an analysis of brightness discrimination as it is influenced by the duration of ΔI. The durations used extend from 0.002 second to 0.5 second. 2. ΔI/I values at constant intensity are highest for the shortest duration and decrease with an increase in duration up to the limits of a critical exposure time. At durations longer than the critical duration the ratio ΔI/I remains constant. 3. The Bunsen-Roscoe law holds for the photolysis due to ΔI. This is shown by the fact that, within the limits of a critical duration, the product of ΔI and exposure time is constant for any value of prevailing intensity, I. 4. At durations greater than the critical duration the Bunsen-Roscoe law is superseded by the relation ΔI = Constant. This change of relation is considered in the light of Hartline''s discussion (1934). 5. The critical duration is a function of intensity. As intensity increases the critical duration decreases. 6. Hecht''s theory (1935) accounts for the data of this experiment if it be assumed that brightness discrimination is determined by a constant amount of photolysis.     

CRITICAL ILLUMINATION AND CRITICAL FREQUENCY FOR RESPONSE TO FLICKERED LIGHT,IN DRAGONFLY LARVAE

Curves relating flicker frequency (F) to mean critical illumination (I_m) for threshold response to flickered light, with equal durations of light and no light intervals, and relating illumination (I) to mean critical flicker frequency (F_m) for the same response, have been obtained from homogeneous data based upon the reactions of dragonfly larvae (Anax junius). These curves exhibit the properties already described in the case of the fish Lepomis. The curve for F_m lies above the curve of I_m by an amount which, as a function of I, can be predicted from a knowledge either of the variation of I_m or of F_m. The law of the observable connection between F and I is properly expressed as a band, not as a simple curve. The variation of I_m (and of F_m) is not due to "experimental error," but is an expression of the variable character of the organism''s capacity to exhibit the reaction which is the basis of the measurements. As in other series of measurements, P.E. _I is a rectilinear function of I_m; P.E. _F passes through a maximum as F (or I) increases. The form of P.E. _F as a function of I can be predicted from the measurements of P.E. _I. It is pointed out that the equations which have been proposed for the interpretation of curves of critical flicker frequency as a function of intensity, based upon the balance of light adaptation and dark adaptation, have in fact the character of "population curves;" and that their contained constants do not have the properties requisite for the consistent application of the view that the shape of the F - I curve is governed by the steady state condition of adaptation. These curves can, however, be understood as resulting from the achievement of a certain level of difference between the average effect of a light flash and its average after effect during the dark interval.     

THE FLICKER RESPONSE CURVE FOR FUNDULUS

After Fundulus heteroclitus have been for some time in the laboratory, under conditions favorable for growth, and after habituation of the fishes to the simple routine manipulations of the observational procedure required, they are found to give reproducible values of the mean critical flash illumination (I_m) resulting in response to visual flicker. The measurements were made with equality of light time and dark time in the flash cycle, at 21.5°C. Log I_m as a function of flash frequency F has the same general form as that obtained with other fishes tested, and for vertebrates typically: the curve is a drawn-out S, with a second inflection at the low I end. In details, however, the curve is somewhat extreme. Its composite form is readily resolved into the two usual parts. Each of these expresses a contribution in which log I, as a function of F, is accurately expressed by taking F as the summation (integral) of a probability distribution of d log I, as for the flicker response contour of other animals. As critical intensity I increases, the contribution of rod elements gradually fades out; this decay also adheres to a probability integral. The rod contribution seen in the curve for Fundulus is larger, absolutely and relatively to that from the cones, than that found with a number of other vertebrates. The additive overlapping of the rod and cone effects therefore produces a comparatively extreme distortion of the resulting F-log I curve. The F-log I_m curve is shifted to lower intensities as result of previous exposure to supranormal temperatures. This effect is only very slowly reversible. The value of F _max. for each of the components of the duplex curve remains unaffected. The rod and cone segments are shifted to the same extent. The persisting increase of excitability thus fails to reveal any chemical or other differentiation of the excitability mechanism in the two groups of elements. Certain bearings of the data upon the theory of the flicker response contour are discussed, with reference to the measurements of variation of critical intensity and to the form of the F-log I curve. The quantitative properties of the data accord with the theory derived from earlier observations on other forms.     

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.     

THEORY AND MEASUREMENT OF VISUAL MECHANISMS : V. FLASH DURATION AND CRITICAL INTENSITY FOR RESPONSE TO FLICKER

The relation between flash duration and mean critical intensity (white light) for threshold recognition of visual flicker, as a function of flash frequency, was investigated by means of measurements at five values of the light-time fraction: 0.10, 0.25, 0.50, 0.75, 0.90, with flash frequencies of the interrupted beam ranging from 2 to 60 per second. A square area, 6.1 x 6.1°, centrally fixated) was viewed monocularly; the discriminometer used provides automatically an artificial pupil 1.8 mm. in diameter. Except for the slight day-to-day fluctuation in the magnitudes of the parameters, the data for the observer used are shown to form an essentially homogeneous group. As for other animals tested, the F - log I_m curve is enlarged and moved toward lower flash intensities as the light-time fraction is decreased. The high intensity segments of the duplex curves are fitted by normal probability integrals for which F _max. and the abscissa of inflection are rectilinear functions of t_L(t_L + t_D), with opposite slopes. The third parameter, (σ''_{log I}, is invariant. The low intensity segments are composites, their shapes determined by the summation of the lower part of the high intensity curve with an overlapping low intensity population of effects. Both the rising and the declining branches of this latter assemblage suffer competitive partial suppression by the effects in the high intensity population. The detailed analysis shows that these results are consistent with the theory of the central, rather than peripheral, location of the dynamically recognizable elements in the determination of flicker.     

CRITICAL INTENSITY AND FLASH DURATION FOR RESPONSE TO FLICKER: WITH ANAX LARVAE

Determinations of the flicker response curve (F – log I_m) with larvae of Anax junius (dragonfly) for various ratios t_L/t_D of light time to dark time in a flash cycle provide relations between t_L/t_D and the parameters of the probability integral fundamentally describing the F – log I function, including the variability of I. These relations are quantitatively of the same form as those found for this function in the sunfish, and are therefore non-specific. Their meaning for the theory of reaction to visual flicker is discussed. The asymmetry of the Anax curve, resulting from mechanical conditions affecting the reception of light by the arthropod eye, is (as predicted) reduced by relative lengthening of the fractional light time in a cycle.     

REACTION TO VISUAL FLICKER IN THE NEWT TRITURUS

The flicker response curve for the newt Triturus viridescens (water phase) has much the same quantitative structure as that found with various fresh-water teleosts at the same temperature (21.5°). The variability of critical intensity and of critical flash frequency likewise follows the same rules. The cone portion of the F - log I curve is much more widely spread, however. This, and the rather low maximum to which the rod curve rises, produce a considerable overlapping of the two parts additively fused. In addition, and to an extent which differs in various individuals, there is apparent a slight departure from the probability integral form of the cone curve. Reasons are given for considering that this is possibly connected with the role of an additional (small) number of (perhaps temporary, or developmental) retinal elements in addition to the typical rods and cones.