FLICKER RESPONSE CONTOURS FOR THE SPARROW,AND THE THEORY OF THE AVIAN PECTEN

The flicker contour for the house sparrow Passer domesticus is duplex, corresponding to the presence of both rods and cones in the retina. The presence of the pecten brings about changes in the "cone" part of the contour when the light-time in the flash cycle is varied. These changes are of the same sort as those we have already described for the visually simplex zebra finch, and for man provided with an artificial "pecten shadow." The changes are such as to greatly enhance flicker acuity for small dark-times (moving stripe technique). The form of the scotopic part of the duplex contour (also as in the case with man) gives no evidence that rod excitation is specifically influenced by the presence of the pecten. The changing integration of "rod" and "cone" effects as the light-time fraction is altered provides another means of testing the theory used for the analytical separation of the two components of the duplex flicker contour.     

THEORY AND MEASUREMENT OF VISUAL MECHANISMS : X. MODIFICATIONS OF THE FLICKER RESPONSE CONTOUR,AND THE SIGNIFICANCE OF THE AVIAN PECTEN

1. When there is projected on the retina (man, monocularly) the shadow of a grid which forms a visual field in several distinct pieces (not including the fovea in the present tests), the ordinary properties of the flicker recognition contour (F vs. log I) as a function of the light-time cycle fraction (t_L) can be markedly disturbed. In the present experiments flicker was produced by the rotation of a cylinder with opaque vertical stripes. In the absence of such a grid shadow the "cone" segments of the contours form a set in which F_max. and the abscissa of inflection are opposite but rectilinear functions of t_L, while the third parameter of the probability integral (σ''_{log I}) remains constant. This is the case also with diverse other animals tested. In the data with the grid, however, analysis shows that even for low values of t_L (up to 0.50) there occurs an enhancement of the production of elements of neural effect, so that F_max. rises rather than falls as ordinarily with increase of t_L, although σ''_{log I} stays constant and hence the total number of acting units is presumed not to change. This constitutes valid evidence for neural integration of effects due to the illumination of separated retinal patches. Beginning at t_L = 0.75, and at 0.90, the slope of the "cone" curve is sharply increased, and the maximum F is far above its position in the absence of the grid. The decrease of σ''_{log I} (the slope constant) signifies, in terms of other information, an increase in the number of acting cone units. The abscissa of inflection is also much lowered, relatively, whereas without the grid it increases as t_L is made larger. These effects correspond subjectively to the fact that at the end-point flicker is most pronounced, on the "cone" curve, along the edges of the grid shadow where contrast is particularly evident with the longer light-times. The "rod" portion of the F - log I contour is not specifically affected by the presence of the grid shadow. Its form is obtainable at t_L = 0.90 free from the influence of summating "cone" contributions, because then almost no overlapping occurs. Analysis shows that when overlapping does occur a certain number of rod units are inhibited by concurrent cone excitation, and that the mean contribution of elements of neural action from each of the non-inhibited units is also reduced to an extent depending on the degree of overlap. The isolated "rod" curve at t_L = 0.90 is quite accurately in the form of a probability integral. The data thus give a new experimental proof of the occurrence of two distinct but interlocking populations of visual effects, and experimentally justify the analytical procedures which have been used to separate them. 2. The changing form of the F - log I contour as a function of t_L, produced in man when the illuminated field is divided into parts by a shadow pattern, is normally found with the bird Taeniopygia castenotis (Gould), the zebra finch. The retina has elements of one general structural type (cones), and the F - log I contour is a simplex symmetrical probability integral. The eye of this bird has a large, complex, and darkly pigmented pecten, which casts a foliated shadow on the retina. The change in form of the F - log I curve occurs with t_L above 0,50, and at t_L = 0.90 is quite extreme. It is more pronounced than the one that is secured in the human data with the particular grid we have used, but there is no doubt that it could be mimicked completely by the use of other grids. The increase of flicker acuity due to the pecten shadow is considerable, when the dark spaces are brief relative to the light. The evidence thus confirms the suggestion (Menner) drawn from comparative natural history that the visual significance of the avian pecten might be to increase the sensory effect of small moving images. It is theoretically important that (as in the human experiment) this may be brought about by an actual decrease of effective retinal area illuminated. It is also significant theoretically that despite the presence of shadows of pecten or of grid, and of the sensory influences thus introduced, the probability integral formulation remains effective.     

THEORY AND MEASUREMENT OF VISUAL MECHANISMS : VI. WAVE-LENGTH AND FLASH DURATION IN FLICKER

For spectral regions associated with violet, blue, green, and red the relation between mean critical flash intensity I_m for visual flicker and the flash frequency F is modified as already found with white light when the light time fraction t_L in the flash cycle is changed. For a square image 6.13° on a side, foveally fixated, the "rod" and "cone" contributions to the duplex contour are analyzed in the way already used for white. It is pointed out that several customary qualitative criteria for cone functioning do not necessarily give concordant results. The analysis shows that the three parameters of the probability summations giving the "rod" and "cone" curves are changed independently as a function of wave-length composition of the light, and of the light time fraction. The correlation of these changes, and of those found in the associated variability functions, can be understood in terms of differences in (1) the numbers of neural units potentially excitable and (2) in the numbers of elements of neural effect obtained from them. In a multivariate situation of this kind it is necessary to compare intensities of luminous flux required to activate half the total population of potentially available elements when this total size is held constant for the different conditions. The results of this comparison, for the filtered lights used, are discussed in relation to certain aspects of excitation vs. wave-length. The problem is a general one, arising where the effects produced as a function of a particular variable are concerned. In the distinction between (1) units excited and (2) the actions they produce may be found the clue for the curious fact that with certain wave-lengths the critical intensities are lower than for white. The extension of the observations to other parts of the retina may be expected to further this analysis.     

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.     

THE FLICKER RESPONSE CONTOUR FOR THE FROG

The flicker response contour for the frog Rana pipiens exhibits the duplex character typical for most vertebrates. By comparison (under the same conditions of temperature, 21.5°, and light-time fraction, = 0.5), the low intensity section of the F - log I curve is the smallest thus far found. The cone portion of the curve is satisfactorily described by a probability integral. The rod part represents the addition of a small group of sensory effects upon the lower end of the cone curve, from which it can be analytically separated. The relation between the two groups of sensory effects permits certain tests of the rule according to which (in homogeneous data) I_m and σ_1I1 are in direct proportion.     

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.     

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.     

OBSERVATIONS ON THE TRANSPORT OF CARBON DIOXIDE IN THE BLOOD OF SOME MARINE INVERTEBRATES

Although the results we have recorded merely serve to indicate the possibilities of this interesting field of investigation, we have sufficient data to enable us to draw certain general conclusions. In the first place it is evident that the bloods of the more highly developed marine invertebrates, such as the active Crustacia and the Cephalopods, are specially adapted for the carriage of carbon dioxide. The quantity of carbon dioxide taken up by the blood of Maia, Palinurus, or Octopus at any given tension of the gas is, in general, about twice or three times as great as that which is taken up by sea water under the same conditions. On the other hand, the blood of a slow, creeping form, such as Aplysia, or of a sessile animal such as the ascidian Phallusia shows no more adaptation for the carriage of carbon dioxide than does sea water. But our estimations of the CO₂ content of the blood as it circulates in the bodies of these more active invertebrates show that the conditions of transport of this gas differ considerably in some respects from those which obtain in mammals. For the invertebrate blood in the body contains only a relatively small quantity of carbon dioxide, averaging in the forms we examined from 3 to 10 cc. per 100 cc. of blood. This forms a marked contrast with the condition found in mammals where even the arterial blood contains about 50 cc. of CO₂ per 100 cc. of blood. The invertebrate, therefore, works at a very low CO₂ tension. There is a twofold significance in this circumstance. In the first place, it means that only the first portion of the carbon dioxide dissociation curve is in use in the respiratory mechanism. Now an inspection of our curves will show that at these low carbon dioxide tensions the dissociation curves tend to be steeper than at higher tensions. As we intend to show in a later paper it can be proved mathematically that, other things being equal, a blood with a carbon dissociation curve of moderate steepness, i.e. one in which the carbon dioxide content of the blood increases fairly rapidly with increase of carbon dioxide tension, is a more efficient carrier of the gas from the tissues to a respiratory surface than a blood in which the dissociation curve is either steeper or flatter. It would seem as if the active invertebrates avoid the use of too flat a part of their CO₂ dissociation curves by working over the initial steeper portion. Furthermore, it is seen that over the range of this initial steep portion of the curves the changes of reaction produced by the uptake of carbon dioxide are much smaller than at higher tensions of the gas; for these initial portions of the curves are more nearly parallel to the lines of constant reaction calculated for a temperature of 15°C. according to Hasselbalch''s method (10) on the assumption that the whole of the combined CO₂ is in the form of sodium bicarbonate. It is evident also that on this assumption the hydrogen ion concentration of the blood of invertebrates (with the exception of the tunicates) would appear to be practically the same as that of the warm-blooded vertebrates—a conclusion confirmed by the direct measurements of Quagliariello (9). On the other hand, our measurements do not lend support to the idea put forward by Collip (4) that in order to maintain an appropriate faintly alkaline reaction an invertebrate needs to retain carbon dioxide in its blood at a comparatively high tension. This idea was based on the observation that at comparatively high CO₂ tensions the blood of invertebrates contains considerably more sodium bicarbonate than does sea water. But our curves show that this is no longer true at the lower values of carbon dioxide tension, the amount of sodium bicarbonate falling off more rapidly in the blood than in the sea water with diminution of the carbon dioxide tension so that in order to maintain an appropriate reaction in the blood only a comparatively small tension of CO₂ is required. The largest amount of carbon dioxide that we found present in the circulating blood of any of the types examined was 9.7 cc. per 100 cc. of blood in the case of Maia, and in most cases the amount was considerably less. But even this lowest value corresponds to a tension of CO₂ of only about 3 mm., so that the tension gradient across the gill membrane must be even less than this. We would emphasize rather the circumstances that as the portion of the dissociation curve over which the reaction is approximately constant is of but small extent, it is necessary that in an active form like Octopus the carbon dioxide produced should be removed rapidly lest an accumulation of it should cause the limits of normal reaction to be exceeded; and this need is correlated with the extreme efficiency of the respiratory apparatus in this animal. It is interesting to notice that the mammal which, in order to obtain an appropriate reaction in the blood, has to work at relatively high carbon dioxide tensions where the dissociation curve is comparatively flat, secures a steeper physiological CO₂ dissociation curve in the body, and with it a more efficient carriage of carbon dioxide and a more constant reaction in the circulating fluid, in virtue of the effect of oxygenation on the carbon dioxide-combining power of its blood (3, 6). Returning now to the consideration of the actual form of the dissociation curves we have obtained—it is a significant fact that it is in those forms such as Maia, Palinurus, and Octopus whose bloods are rich in proteins—particularly hemocyanine—that the initial steep portion of the curve is observed. This suggests that in these forms the blood proteins act as weak acids and expel carbon dioxide from the blood at the low tensions which include the physiological range, just as in vertebrates the hemoglobin similarly displaces carbonic acid from its combination with alkali metal. On the other hand the cœlomic fluid of Aplysia contains no pigment and only 0.00672 per cent of protein nitrogen (Bottazzi (11)) and shows no initial rapidly ascending portion of the CO₂ dissociation curve. This is supported by the observation of Quagliariello (9) that the acid-neutralising power of the blood of an invertebrate is roughly proportional to its protein content. It seems as if the proteins of invertebrate blood like the blood proteins of vertebrates, exist in the form of sodium salts which are capable of giving up sodium for the transport of carbon dioxide as sodium bicarbonate. That this is so in the case of hemocyanine follows from the fact that the isoelectric point of this pigment occurs at a hydrogen ion concentration of 2.12 x 10^–5 N, i.e. at a pH of 4.67 (Quagliariello (12)) so that in the alkaline blood of the invertebrates possessing it, hemocyanine will act as a weak acid. It is probable that the initial steep portion of the carbon dioxide dissociation curves which we have found to be of such importance in the respiration physiology of Octopus, Palinurus, and Maia is produced by the competition of this acid with carbonic acid for the available sodium of the blood.     

THE ORIGIN OF THE POTENTIAL DIFFERENCES RESPONSIBLE FOR ANOMALOUS OSMOSIS

1. Collodion bags coated with gelatin on the inside were filled with a M/256 solution of neutral salt (e.g., NaCl, CaCl₂, CeCl₃, or Na₂SO₄) made up in various concentrations of HNO₃ (varying from N/50,000 to N/100). Each collodion bag was put into an HNO₃ solution of the same concentration as that inside the bag but containing no salt. In this case water diffuses from the outside solution (containing no salt) into the inside solution (containing the salt) with a relative initial velocity which can be expressed by the following rules: (a) Water diffuses into the salt solution as if the particles of water were negatively charged and as if they were attracted by the cation and repelled by the anion of the salt with a force increasing with the valency of the ion. (b) The initial rate of the diffusion of water is a minimum at the hydrogen ion concentration of about N/50,000 HCl (pH 4.7, which is the point at which gelatin is not ionized), rises with increasing hydrogen ion concentration until it reaches a maximum and then diminishes again with a further rise in the initial hydrogen ion concentration. 2. The potential differences between the salt solution and the outside solution (originally free from salt) were measured after the diffusion had been going on for 1 hour; and when these values were plotted as ordinates over the original pH as abscissae, the curves obtained were found to be similar to the osmotic rate curves. This confirms the view expressed by Girard) Bernstein, Bartell, and Freundlich that these cases of anomalous osmosis are in reality cases of electrical endosmose where the driving force is a P.D. between the opposite sides of the membrane. 3. The question arose as to the origin of these P. D. and it was found that the P.D. has apparently a double origin. Certain features of the P.D. curve, such as the rise and fall with varying pH, seem to be the consequence of a Donnan equilibrium which leads to some of the free HNO₃ being forced from the solution containing salt into the outside solution containing no (or less) salt. This difference of the concentration of HNO₃, on the opposite sides of the membrane leads to a P.D. which in conformity with Nernst''s theory of concentration cells should be equal to 58 x (pH inside minus pH outside) millivolts at 18°C. The curves of the values of (pH inside minus pH outside) when plotted as ordinates over the original pH as abscissae lead to curves resembling those for the P. D. in regard to location of minimum and maximum. 4. A second source of the P.D. seems to be diffusion potentials, which exist even if no membranes are present and which seem to be responsible for the fact that the rate of diffusion of negatively charged water into the salt solution increases with the valency of the cation and diminishes with the valency of the anion of the salt. 5. The experiments suggest the possibility that the establishment of a Donnan equilibrium between membrane and solution is one of the factors determining the Helmholtzian electrical double layer, at least in the conditions of our experiments.     

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.     

THE FLICKER RESPONSE CONTOUR FOR THE ISOPOD ASELLUS

The flicker response contour for the isopod Asellus is a simple probability integral (F - log I) over the whole determinable range (F = 1 to 51). This contrasts with the "distorted" asymmetrical curves obtained with Apis, Anax, and other arthropods with large convex eyes. The explanation of the distortion as due to mechanical conditions affecting photoreception is therefore confirmed, as the structure of the Asellus eye does not make such a factor likely to be expected for this case. The Asellus curve agrees with the only other available complete and uncomplicated flicker response contour (from Pseudemys, turtle with rod-free retina), in showing the superiority of the probability integral formulation as compared with certain others which have been suggested. It is noted as a curious and probably important fact that the relative dispersion of the intensity thresholds (σ''_{log I}) for the elements implicated in determining the flicker contour appears to be identical in bee, dragon fly nymph, and isopod. Other relevant information derived from similar experiments with vertebrates shows that this quantity is specifically determined by the organization of the animal. The nature of the common feature of neural organization in three such diverse arthropods, as contrasted with the diversity seen within one class of vertebrates (e.g., teleosts), remains to be discovered.     

AMPHOTERIC COLLOIDS : V. THE INFLUENCE OF THE VALENCY OF ANIONS UPON THE PHYSICAL PROPERTIES OF GELATIN.

1. When we plot the values of osmotic pressure, swelling, and viscosity of gelatin solutions as ordinates over the pH as abscissæ, practically identical curves are obtained for the effect of monobasic acids (HCl, HBr, HNO₃, and acetic acid) on these properties. 2. The curves obtained for the effect of H₂SO₄ on gelatin are much lower than those obtained for the effect of monobasic acids, the ratio of maximal osmotic pressures of a 1 per cent solution of gelatin sulfate and gelatin bromide being about 3:8. The same ratio had been found for the ratio of maximal osmotic pressures of calcium and sodium gelatinate. 3. The curves representing the influence of other dibasic and tribasic acids, viz. oxalic, tartaric, succinic, citric, and phosphoric, upon gelatin are almost identical with those representing the effect of monobasic acids. 4. The facts mentioned under (2) and (3) permit us to decide between a purely chemical and a colloidal explanation of the influence of acids on the physical properties of gelatin. In the former case we should be able to prove, first, that twice as many molecules of HBr as of H₂SO₄ combine with a given mass of gelatin; and, second, that the same number of molecules of phosphoric, citric, oxalic, tartaric, and succinic acids as of HNO₃ or HCl combine with the same mass of gelatin. It is shown in the present paper that this is actually the case. 5. It is shown that gelatin sulfate and gelatin bromide solutions of the same pH have practically the same conductivity. This disproves the assumption of colloid chemists that the difference in the effect of bromides and sulfates on the physical properties of gelatin is due to a different ionizing and hydratating effect of the two acids upon the protein molecule.     

A STUDY OF THE BACTERICIDAL ACTION OF ULTRA VIOLET LIGHT : I. THE REACTION TO MONOCHROMATIC RADIATIONS

In this first paper of a series on the bactericidal action of ultra violet light the methods of isolating and measuring monochromatic radiations, of preparing and exposing the bacteria, and of estimating the effects of exposure, are given in detail. At all the different wave lengths studied the reactions of S. aureus followed similar curves, but occurred, at each wave length, at a different energy level. The general similarity of these curves to those for monomolecular reactions provokes a discussion of their signifiance, and emphasis is laid upon variations in susceptibility of individual organisms, due especially to age and metabolic activity, so that the typical curve seems to be best interpreted as one of probability.     

THE SPECTRAL SENSIBILITY OF THE SUN-FISH AS EVIDENCE FOR A DOUBLE VISUAL SYSTEM

1. An extension of a previously described method makes possible the measurement of the visibility function of Lepomis at high intensities of spectral illumination. This is accomplished by determining the relative energies of various spectral beams which will just produce a visual orienting response by the animal to the movement of a pattern composed of fine lines. 2. The function so determined is different from that obtained with a pattern composed of wide bars and spaces at a lower intensity level. 3. This difference furnishes direct and quantitative proof that the eye of Lepomis is a physiologically duplex visual system and parallels the known anatomical distinctions between the rods and cones. 4. A comparison of the visibility curves of the two systems indicates that both functions are similar in shape but that the cone curve is shifted to the red. 5. It is suggested that this relation between the two systems, which is also found in the human and the fowl, indicates that the photosensory substance is the same in each case for the rods and cones. According to this hypothesis, the shift of the cone curve is due to a common physical cause which depends on differences in the properties of the solvent media in the cones and in the rods.     

THE FLICKER RESPONSE CONTOUR FOR THE CRAYFISH. I

The F - log I curve for threshold response to visual flicker has been determined for the crayfish Cambarus bartoni. As predicted on the basis of the higher curvature of the optic surface, the flicker response contour is more asymmetrical than for bee and dragonfly nymph under comparable conditions of temperature and light time fraction of flash cycle. The mechanical origin of this asymmetry is thus confirmed, and is further supported by the similar forms of the F - log I curves in bee, dragonfly larva, and crayfish in the lower portion of the curves (up to F = 70 per cent F_max.). The slope of the fundamental curve for crayfish, deduced by analysis of the data, is lower than for bee, dragonfly nymph, or Asellus. This signifies a wider spread of the effective distribution of elemental log I thresholds involvable in the response to flicker, and may be traced either to the greater curvature of the eye-surfaces or to their position upon movable pedicles. The results are therefore consistent with the statistical conception of the nature of effects recognizable as due to the activity of excitable elements.     

THE FLICKER RESPONSE CONTOURS FOR GENETICALLY RELATED FISHES. II

The flicker response contour has been determined for several species and types of the teleosts Xiphophorus (X.) and Platypoecilius (P.) under the same conditions. The curve (F vs. log I_m) is the same for representatives of each generic type, but is different for the two genera. Its duplex nature is analyzable in each instance by application of the probability integral equation to the rod and cone constituent parts. The parameters of this function provide rational measures of invariant properties of the curves, which have specific values according to the genetic constitution of the animal. The F ₁ hybrids (H'''') of X. montezuma x P. variatus show dominance of the X. properties with respect to cone F_max. and σ'' _{log I}, but an intermediate value of the abscissa of inflection (τ''). The rod segment shows dominance of σ'' _{log I} from P., but an intermediate value of F_max. and of τ''. The composite flicker curve involves the operation of two distinct assemblages of excitable elements, differing quantitatively but not qualitatively in physicochemical organization, probably only secondarily related to the histological differentiation of rods and cones because almost certainly of central nervous locus, but following different rules in hereditary determination, and therefore necessarily different in physical organization. The interpretation of the diverse behavior of the three parameters of the probability summation is discussed, particularly in relation to the physical significance of these parameters as revealed by their quantitative relations to temperature, retinal area, and light time fraction in the flash cycle, and to their interrelations in producing the decline of rod effects at higher intensities. It is stressed that in general the properties of the parameters of a chosen interpretive analytical function must be shown experimentally to possess the physical properties implied by the equation selected before the equation can be regarded as describing those invariant properties of the organic system concerned upon which alone can deduction of the nature of the system proceed. The importance of genetic procedures in furthering demonstration that the biological performance considered in any particular case exhibits constitutionally invariant features provides a potentially powerful instrument in such rational analysis.     

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.