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1-20 of 48

Ernst Wolf

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Journal Articles

Journal:
Journal of General Physiology

*Journal of General Physiology*(1944) 27 (6): 513–528.

Published: 20 July 1944

Abstract

Flicker contours from vertebrates (fishes to man) show that the slope parameter σ' log I in the efficiently descriptive probability summation 100 F/F max. = ∫ –inf; log I e –(log I/I i ) –(log I/I i )2 /2(σ') /2(σ')2 · d log I is distributed bimodally (simple fields, "white" light), from 0.60 to 2.3, with well defined peaks at 0.80 and 1.75. This parameter is independent of F max. , log I i , temperature, light-time fraction, and in general not greatly influenced by λ. "Rod" components of known visually duplex contours, without exception, and some "cone" contours, are in the first group; an equal number of "cone" curves are in the second group, together with one simplex "rod" contour; purely cone contours are in each group, as well as cone segments of duplex curves. No firm zoological grouping of the "cone" curves can be made, on present evidence,—although the 5 fishes used give high-slope curves, 2 amphibians low slopes, reptiles (5) either high or low, birds (2) and anthropoids (2) low-slope "cone" curves. By subdivision of the visual image and by change of wave-length, under certain conditions, in man, and by use of the "pecten effect" in birds (and man), cone contours of the low-slope class can be transformed into curves of the high-slope group. These procedures do not fundamentally change the "rod" slopes. Consequently, although under simple conditions they are specifically determined, the forms of the F - log I contour cannot be used as diagnostic for rod or cone functioning. It is reinforced, by new data on Anolis (lizard) and Trionyx (turtle), that an obviously duplex retina is specifically correlated with a duplex performance contour, a simplex retina with a simplex one. But no support is given to the view that the shapes of these curves are diagnostic of differences in rod or cone fundamental excitabilities, or that they describe properties of these units. In visual duplexity we have to do simply with the fact that two groups of neural effects are available; it is with their properties that we deal in measurements of duplex visual excitability.

Journal Articles

Journal:
Journal of General Physiology

*Journal of General Physiology*(1944) 27 (5): 401–432.

Published: 20 May 1944

Abstract

Flicker contours for a square image of 3° visual angle, centered 6° on the temporal side of the fovea, the light sectored at a focus, are strikingly modified if the same illuminated area is arranged in four squares separated by a narrow opaque cross. The "cone" curves are made much steeper, and their abscissae of inflection (τ' are at higher intensities; F max. is not greatly changed, but alters less with change of light-time fraction in the flash cycle ( t L ). This modification is accompanied by a great enlargement of the scotopic segment of the duplex curves, consistent with the theory of the integrative relations of neural effects in the two groups of units involved. The changes are not consistent with the view that flicker end-points are determined by the activation of retinal cells with a fixed spatial distribution of invariable thresholds. At t L = 0.50 the 3° subdivided area gives very nearly the same contour as does a square 6° x 6°, with the same total perimeter of light-dark separation; the "edge effect" thus suggested is complicated by differences in the dependence of F max. and τ' upon t L . When an image pattern is produced by a grid of light bars separated by equally broad opaque spaces (10° x 10° over-all, centered at the fovea), the photopic flicker contours are made very steep and their midpoints are situated at quite low intensities, while the "rod" contribution tends to be more completely fused with the "cone" than is found for fields not subdivided. However, instead of a progressive increase of τ' with t L the curves for t L = 0.75 and 0.90 lie respectively below that for t L = 0.25 and 0.50 for a field of four broader stripes (1.43°) and both are below t L = 0.25 for a field of seven narrower stripes (0.77°). These latter changes are discussed in terms of the participation of subsidiary phenomena involving so called "γ movement." It is pointed out that since in these data σ 1 / I m is for each set of conditions a statistically constant quantity with a characteristic breadth of scatter σ σ , it is possible to calculate a "coefficient of internal correlation" r which is a function of the conditions (as: image area, location, wave length of light, structure of image, light-time fraction) and which describes a property of any entire contour. The changes in r , as a function of the conditions of flicker excitation, reflect changes in the neural organization responsible for the liminal discrimination of flicker. It is shown that as consequence of simple changes in the image field, three parameters, as of the probability summation, are required for the description of a simplex flicker contour—since each of these is independently modifiable as to its magnitude and in its dependence on the light-time fraction. Subdivision of the image, with light sectored at a focus, produces in part only the changes in the flicker contour which we have earlier labelled the "pecten effect." In the latter, with light not sectored at a focus but with bar images moving across a field with inclined fixed opaque bars, the "cone" slope ( dF/d log I ) is sharply increased for t L > 0.50, but not below t L = 0.50, and the value of τ' is much less than it "should be." Consequently, the change in contrast brought about by the moving contact of light/dark borders is the significant factor in the "pecten effect," not simply pulsatile interruption of the light.

Journal Articles

Journal:
Journal of General Physiology

*Journal of General Physiology*(1944) 27 (5): 481.

Published: 20 May 1944

Abstract

In Vol. 27, No. 5, May 20, 1944, page 403, in the eighth line from the bottom of the page, the comma after "intensity" should be a semicolon. On page 413, in the second formula from the bottom of the page, for See PDF for Equation read See PDF for Equation On the same page, formula 2 should read See PDF for Equation On page 414, line 3, at the end of the line add "or" to read "of the level of I or of F ." On page 422, in the first line below the figure legend, for "illuminate" read "illuminated." On page 430, line 22, for "lighteb dars" read "lighted bars."

Journal Articles

Journal:
Journal of General Physiology

*Journal of General Physiology*(1944) 27 (4): 315–324.

Published: 20 March 1944

Abstract

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.

Journal Articles

Journal:
Journal of General Physiology

*Journal of General Physiology*(1944) 27 (4): 287–313.

Published: 20 March 1944

Abstract

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.

Journal Articles

Journal:
Journal of General Physiology

*Journal of General Physiology*(1943) 27 (2): 119–138.

Published: 20 November 1943

Abstract

Flicker response contours ( F vs . log I m ) for a square image subtending 0.602° on a side, located in the fovea, are simplex probability integrals for a "white" and for four (five) spectral regions filtered from this white, and with different light-time fractions in the flash cycle. The subjective phenomena (the appearance of the field, the intensity threshold for color, and others) at the fusion points along these contours parallel in a variety of ways those obtained on duplex flicker contours resulting from the use of larger or eccentrically placed flickered images. These phenomena therefore cannot be held to indicate involvements of "rod" excitation. The scatter of the index of variation of I 1 is such as to demonstrate the full participation of all the potentially excitable neural units at all levels of flash frequency, for each kind of light. The magnitude of this scatter, a measure of neural integration in visual performance, is a function of the number of these units (with F max. nearly constant); the two quantities vary together when wave-length composition of light is altered. The properties of the contours for a white light and for the spectral regions filtered from it show that, for the image within the fovea, different numbers of units are excitable in flicker recognition according to the wave-length band used, and different mean frequencies of elements of effect under fixed conditions. The changes in the mean intensity for activation of these units as a function of the light-time fraction in the flash cycle are correlated with the numbers of these units; when this is corrected for, it is pointed out that despite the differences in shape of F vs . log I it cannot be concluded that the mechanism of excitation differs for different wave-lengths. It is indicated that "white" must be regarded as a synthesis, not a mere summation, of effects due to different spectral regions. Certain differences are pointed to as between foveal and more peripheral regions tested, and as between observers differing in the degree of the "yellow spot effect," with regard to the relative effects of wave-length and of image area. A general consequence is the outlining of conditions required for the precise comparison of excitabilities as a function of wave-length in the multivariate visual system.

Journal Articles

Journal:
Journal of General Physiology

*Journal of General Physiology*(1942) 25 (3): 369–379.

Published: 20 January 1942

Abstract

Flicker response curves (man) obtained with images formed entirely within the fovea are like those secured with lower animals having only one general class of retinal receptors. They are normal probability integrals ( F vs . log I m ), and the properties of their parameters agree with those for visually simplex animals and for the "cone" portions of contours exhibiting visual duplexity. By several different procedures, involving experimental modifications of the "cone" curve, the "rod" part of the typical human duplex curve can be obtained free from overlapping by the extrapolated "cone" curve. It then has the probability integral form which the lower segment does not directly exhibit when combined with "cone" effects. These results are discussed with reference to the statistical nature of the fundamental form of the flicker contour and to the interpretation of duplex curves produced by the neural integration of two independently modifiable groups of sensory effects.

Journal Articles

Journal:
Journal of General Physiology

*Journal of General Physiology*(1942) 25 (3): 381–390.

Published: 20 January 1942

Abstract

With lights of different spectral compositions filtered from a white, the flicker response contours for the zebra finch are found to exhibit the same general kind of relationship between flicker excitation and wavelength as is found in the case of man ("cone" contours), with the same filters. The flicker contours for the zebra finch are simplex; the retina contains no rods. On a relative energy scale, with a flash cycle of fixed light-time percentage (10 per cent) the curve for yellow almost coincides with that for the white, the curve for red lies at much higher intensities, and the curves for blue-green and violet fall below that for the white by amounts increasing in that order. The maxima to which the curves rise and the slope constants are very nearly the same for all the spectral regions. For the bird the blue was a little less efficient, the green a little more efficient, and the red very much less efficient than in the case of man. It was deduced that in the retina of this diurnal bird the number of red oil globules should be comparatively small and that most of the globules should be greenish yellow. This was confirmed by direct examination.

Journal Articles

Journal:
Journal of General Physiology

*Journal of General Physiology*(1941) 25 (2): 293–308.

Published: 20 November 1941

Abstract

The several parameters of the flicker response contour ( F – log I ) are considered as a function of wave-length composition (white, blue, and red) and light-time fraction, for an extra-foveal region (monocular, temporal retina). These data are compared with those secured for the same image area centrally fixated at the fovea. The systematic changes in the parameters are shown to be in rational relation to other relevant excitability data. Since for two retinal regions the primary contours are quite different, the systematic nature of the behavior of the parameters in the two cases is a real test of the power of the analysis proposed. Theoretical interpretation is required to deal with the properties of sets of performance contours under systematically varied conditions, and cannot rely simply on the comparison of (for example) two contours under the same arbitrary conditions at two retinal locations. In particular it is emphasized that a qualitative separation must be made of the two factors of ( a ) number of units and ( b ) the frequencies of their actions, before the wave-length problem can be dealt with effectively.

Journal Articles

Journal:
Journal of General Physiology

*Journal of General Physiology*(1941) 25 (1): 89–110.

Published: 20 September 1941

Abstract

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.

Journal Articles

Journal:
Journal of General Physiology

*Journal of General Physiology*(1941) 24 (5): 635–654.

Published: 20 May 1941

Abstract

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.

Journal Articles

Journal:
Journal of General Physiology

*Journal of General Physiology*(1941) 24 (5): 625–633.

Published: 20 May 1941

Abstract

The flicker response contour has been determined, with equality of light-dark time ratio, for the diurnal bird the Australian zebra finch. This bird has only cones in the retina. The curve of log critical intensity as a function of flash frequency is simplex, a normal probability integral. In this respect it is like that for other vertebrates not exhibiting visual duplexity. The parameters of the curve most closely approach those for the turtle Pseudemys (extrapolated to about the same temperature); it is not improbable that the approximation of these two curves would be less close for other values of the light-time fraction. Some points of interpretive visual theory are discussed in relation to the present measurements.

Journal Articles

Journal:
Journal of General Physiology

*Journal of General Physiology*(1941) 24 (4): 505–534.

Published: 20 March 1941

Abstract

Comparison of monocular and binocular critical flash intensities for recognition of flicker, using a centrally fixated square image subtending ca . 6.13° on a side (white light), shows that for the cone segment of the response contour the inflection point of the probability integral correlating flash frequency F (for symmetrical flicker) and log mean critical flash intensity I m is with the binocular measurements exactly intermediate between those for each eye separately. This does not mean that in general the data are intermediate; they are not; the binocular asymptotic F max. agrees with or lies above the greater one of the two uniocular curves. The entire contour must be considered for valid intercomparisons, as is also true if homologous curves for different observers are to be compared. For the measurements in the predominantly rod region the binocular data are more or less intermediate. The rod curves result, however, from the integrative interplay of rod and cone effects for which the intrinsic curves overlap. The resultant rod curve as measured is determined by the partial inhibition of rod effects by cone effects, and by the summation of the remaining rod contributions with those labelled cone in origin. It is pointed out that in this respect, as in others, it is desirable to consider the rôles of retinal area, and location, from the standpoint of integration of neural effects. These phenomena are essentially independent of the light-time fraction and of the spectral (λ) quality of the light used. For binocular, as for uniocular excitation, the normal probability summation provides an efficient general description, under diverse conditions of size and location of retinal image, wave-length composition of light, light-time cycle-fraction, and kind of animal. It is pointed out that this is the only function abstractly likely to exhibit this kind of efficiency. That a summation of veritable effects independently generated by simultaneous, symmetrical uniocular excitation does occur in the recognition of flicker is specifically demonstrated by the fact that for a given mean critical flash intensity the associated variation is lower for binocular than for either or the average of the single-eyed presentations,—and in the ratio not statistically different from 1:1.41; the relative scatter of the binocular indices of dispersion is also reduced below the uniocular. Since the mean variation of the critical intensity is statistically in a constant ratio to I m , in appropriately homogeneous series, independent for example of the brightness level and of the light-time fraction, this signifies an essential doubling of the effectiveness (potential) of each of the elements concerned in the discrimination of flicker when binocular excitation is concerned, although the total number of these elements is only slightly or not at all affected. The potential in question is not exclusively correlated with subjective brightness-at-fusion, which is, however, increased with binocular regard.

Journal Articles

Journal:
Journal of General Physiology

*Journal of General Physiology*(1941) 24 (3): 317–324.

Published: 20 January 1941

Abstract

The lizard Phrynosoma , with purely cone retina, provides a simplex flicker response contour (log critical flash intensity as a function of flash frequency). It is well described as a normal probability integral ( F - log I ). The Phrynosoma curve differs markedly, in higher slope and in higher median intensity level, from that obtained under the same conditions for the turtle Pseudemys , also with entirely cone retina. Other comparisons having a bearing on the duplexity doctrine are discussed.

Journal Articles

Journal:
Journal of General Physiology

*Journal of General Physiology*(1940) 23 (6): 677–694.

Published: 20 July 1940

Abstract

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.

Journal Articles

Journal:
Journal of General Physiology

*Journal of General Physiology*(1940) 23 (6): 667–676.

Published: 20 July 1940

Abstract

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.

Journal Articles

Journal:
Journal of General Physiology

*Journal of General Physiology*(1940) 23 (5): 531–549.

Published: 20 May 1940

Abstract

For the turtle Pseudemys scripta the temperature characteristics for excitability of the response to visual flicker are found to be independent of flash frequency F , flash intensity I , and proportion of light time in the flash cycle. The maximum F to which the flicker response contour ( F vs . log I ) rises, and the abscissa of its inflection, are rectilinear functions of the percentage light-time in the flash cycle, but µ for 1/ I at any flash frequency is the same with different values of the percentage light-time (10 to 90 per cent). These facts, together with the properties of the variation of the critical intensity, objectively demonstrate the essentially simple or unitary character of the controlling events in the mechanism governing the excitability. They also provide a means of further illustrating a procedure whereby certain statistical factors in the performance of a population of units may be analytically separated from excitability properties common to all of the individual units. In particular, it is of general significance that it can be seen how it is possible for biologically exhibited frequencies or rates of performance to provide simple and physically significant relations to temperature, despite the fact that this performance may involve, almost inevitably does involve, the integrated actions of many individual units.

Journal Articles

Journal:
Journal of General Physiology

*Journal of General Physiology*(1939) 23 (2): 229–237.

Published: 20 November 1939

Abstract

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 1 I 1 are in direct proportion.

Journal Articles

Journal:
Journal of General Physiology

*Journal of General Physiology*(1939) 23 (2): 143–163.

Published: 20 November 1939

Abstract

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.

Journal Articles

Journal:
Journal of General Physiology

*Journal of General Physiology*(1939) 23 (1): 1–10.

Published: 20 September 1939

Abstract

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.