The normal rate of growth of the specimen in the dark was 047 per second; this was reduced to 029 under an intensity of one unit, to 017 under two, and to 010 under three units. Growth became arrested when the intensity was raised to four units. Thus increasing intensity of light induces an increasing r.e.t.a.r.dation of growth at the proximal side of the organ. This aided by the effect of indirect stimulus at the distal side brings about an increasing positive curvature.

_Experiment 130._--The flower bud of _Crinum_ was used for the experiment, the source of light being a small arc lamp. The duration of exposure was one minute. Increasing intensity of light gave rise to increasing positive curvatures (Fig. 125) in the ratio of 1:25:5 under increasing intensities which varied as 1:2:3.

THE EFFECT OF INCREASING ANGLE.

The quant.i.ty of light which falls on an unit area of the responding organ varies as sin [Greek: th] where [Greek: th] is the directive angle _i.e._ the angle made by the rays with the surface. Some allowance has to be made for the amount of light reflected from the surface, this being greater at 45 than at 90.

[Ill.u.s.tration: FIG. 126.--The Collimator.]

_Tropic response of pulvinus of_ Desmodium gyrans: _Experiment 131._--For application of light at various angles an incandescent electric lamp was mounted at one end of a bra.s.s tube, a collimating lens being placed at the other (Fig. 126). The parallel beam of light from the collimator could be sent at various angles by rotating the collimator tube round an axis at right angles to the tube. The specimen employed was the terminal leaflet of _Desmodium gyrans_; light was applied for a minute in the two successive experiments for the two angles of 45 and 90. The record (Fig. 127) shows that the phototropic effect increases with the directive angle. In the present case the ratio of the two effects is 16:1, which is not very different from the ratio sin 90/sin 45 = 14.

[Ill.u.s.tration: FIG. 127.--Effect of angle of inclination of light on the tropic curvature of pulvinus. The first response is to light at 45 and the second, to 90. (_Desmodium gyrans_).]

[Ill.u.s.tration: FIG. 128.--Series of tropic curvatures of growing bud of _Crinum_ to alternate stimulation by light at 45 and 90.]

_Tropic response of growing organs: Experiment 132._--Similar experiment was carried out with the flower bud of _Crinum_, held vertical. Light was applied alternately at 45 and 90, in two successive series. The object of this was to make due allowance of possible variation of excitability of the organ during the course of the experiment. I have explained (p. 147), how the excitability of a tissue in a condition slightly below par, is increased by the action of previous stimulation.

Series of responses obtained under alternate stimulations at 45 and 90 enable us to find out, whether any variation of excitability occurred during the course of the experiment and make allowance for it.

The records show that stimulation did enhance the excitability of the organ to a small extent. Thus the first stimulation at 45 induced an amplitude of response of 5 mm.; the second stimulation at 45 _i.e._ the third response of the series, induced a slightly larger response 7 mm.

in amplitude. Similarly the two responses at 90 gave an amplitude of 9 mm. and 11 mm. respectively (Fig. 128). Taking the mean value of each pair, the ratio of tropic effects for 90 and 45 is = 10/6 = 17 nearly.

EFFECT OF DURATION OF EXPOSURE.

_Experiment 133._--The specimen employed for the experiment was a flower bud of _Crinum_ in a slightly sub-tonic condition. Successive responses exhibited on this account, a preliminary negative[15] before the normal positive curvature. The successive durations of exposure were for 1, 2, and 3 minutes. The amplitudes of responses (Fig. 129) are in the ratio of 1:25:5.

[15] An explanation of this preliminary effect will be found in the next chapter.

[Ill.u.s.tration: FIG. 129.--Effect of increasing duration of exposure 1:2:3 minutes, on phototropic curvature. Note preliminary negative response. (_Crinum_).]

We may now recapitulate the tropic effects of light of increasing intensity, directive angle, and duration of exposure. It has been shown that the tropic effect is enhanced under increasing intensity of light; it is also increased with the angle increasing from grazing to perpendicular incidence. And finally, the tropic effect is enhanced with the duration of exposure. Taking into consideration the effects of these different factors we arrive at the conclusion that _phototropic effect increases with the quant.i.ty of incident light_. It will be shown in the next chapter that strict proportionality of cause and effect holds good in the median range of stimulation, and the slight deviation from this, above and below the median range, is due to the fact that susceptibility for excitation is low at these two regions.

SUMMARY.

Increasing intensity of light induces increasing tropic curvature.

Tropic curvature increases with the directive angle, the effect being approximately proportional to sin [Greek: th], where [Greek: th] is the angle made by the rays with the responding surface.

Tropic curvature also increases with the duration of exposure.

The intensity of induced tropic effect is determined by the quant.i.ty of incident light.

x.x.xII.--THE PHOTOTROPIC CURVE AND ITS CHARACTERISTICS

_By_

SIR J. C. BOSE.

When a plant organ is subjected to the continued action of unilateral stimulus of light, it exhibits increasing tropic curvature, which in certain cases reaches a limit; in other instances a reversal takes place, seen in neutralisation, or in the conversion of the positive into negative curvature. I shall in this chapter enter into a detailed study of the phototropic curve, and determine its characteristics.

As the vague terminology at present in use has been the source of much confusion, it is necessary here to define clearly the various terms which will be employed in this investigation. It is first of all necessary to distinguish between cause and effect, between external stimulus and the excitation induced by it. As regards stimulus itself I have shown elsewhere[16] that its effective intensity becomes summated by repet.i.tion. This was demonstrated by the two following typical experiments carried out with the pulvinus of _Mimosa_.

[16] "Irritability of Plants"--p. 54.

(1) The intensity of a single electric shock of intensity of 05 unit was found to be ineffective in inducing excitation; but it became effective on being repeated four times in rapid succession.

(2) The same specimen was next subjected to a feebler stimulus of intensity of 01 unit, and it required a repet.i.tion of 20 times for the stimulus to become effective.

The total stimulus in the first case was 05 4 = 2, and this was found to be the same as 01 20 = 2 in the second case. Thus the intensity of stimulus is increased by repet.i.tion; in the limiting case where the interval between successive stimulus is zero, the stimulus becomes continuous. Bearing in mind the additive effects of stimulus we see that its effective intensity increases with the _duration_ of application.

This important conclusion found independent support from the results of Experiment 133 given in the last chapter.

We shall now take up the general question of the characteristics of the phototropic curve, which gives the relation between increasing stimulus and the resulting excitation. As regards stimulus we found that its effectiveness increases with the duration of application. The induced excitation in growing organs may be measured by concomitant r.e.t.a.r.dation of growth caused by stimulus. In the excitation curves which will be presently given, the abscissae represent increasing stimulus and ordinates the resulting excitation. This excitation curve may be obtained by making the plant record on a moving plate its r.e.t.a.r.dation of growth by means of the High Magnification Crescograph. I reproduce below two records of the effects of continuous photic and electric stimulation. The ordinate of the 'excitation curve' (Fig. 130) exhibits increasing incipient contraction (r.e.t.a.r.dation of growth) culminating in an arrest of growth; the abscissa represents increasing stimulus consequent on increased duration of application. The record shows that the incipient contraction is slight at the first stage; it increases rapidly in the second stage; finally, it declines and reaches a limit.

The excitatory reaction is thus not constant throughout the entire curve of excitation, but undergoes very definite and characteristic changes.

We shall find similar characteristics in the phototropic curves under unilateral stimulus which will be given presently. The explanation of the similarity is found in the fact that the tropic curvature is also due to incipient contraction or r.e.t.a.r.dation of the rate of growth, which remains confined to the directly stimulated proximal side of the organ.

[Ill.u.s.tration: FIG. 130.--Effects of continuous (_a_) electric, and (_b_) photic stimulation on rate of growth. Abscissa represents duration of application of stimulus. Note induced r.e.t.a.r.dation, and arrest of growth.]

For facility of explanation of what follows, I shall have to use a new and necessary term, _susceptibility_, to indicate the relation of cause and effect, of stimulus and resulting excitation. _Susceptibility_ is thus = Excitation/Stimulus. Different organs of plants exhibit unequal susceptibilities; some undergo excitation under feeble stimulus, while others require more intense stimulus to induce excitation. But even in an identical organ the susceptibility undergoes, as we have seen, a characteristic variation, being feeble at the beginning of the excitation curve, considerable in the middle, and becoming feeble once more towards the end of the curve. The most difficult problem that faces us is an explanation of this characteristic difference in different parts of the tropic curve.

GENERAL CONSIDERATIONS.

Before entering into the fuller consideration of the subject, it will be helpful to form some mental picture of the phenomena of excitation, however inadequate it may be. The excitation is admitted to be due to the molecular upset induced by the shock of stimulus[17]; the increased excitation results from increasing molecular upset brought on by enhanced stimulus. The condition of molecular upset or excitation may be detected from the record of any one of the several concomitant changes, such as the change of form, (contraction or expansion) or change of electric condition (galvanometric negativity or positivity). These means of investigation are not in principle different from those we employ in the detection of molecular distortion in inorganic matter under increasing intensities of an external force.

[17] I shall use the term _stimulus_ in preference to _stimulation_, for the latter is often taken in the sense of the resulting excitation.

THE CHARACTERISTIC CURVE.

Thus the molecular upset and rearrangement, in a magnetic substance under increasing magnetising force are inferred from the curve obtained by means of appropriate magnetometric or galvanometric methods. I reproduce the characteristic curve of iron (Fig. 131) in which the abscissa represents increasing magnetising force, and the ordinate, the induced magnetisation. This characteristic curve, giving the relation of cause and effect, will be found to be highly suggestive as regards the similar characteristic curve which gives the relation between increasing stimulus and the resulting enhanced tropic effect in vegetable tissues.

The parallelism will be found to be very striking.

Inspection of figure 131 shows that, broadly speaking, the curve of magnetisation may be divided into four parts. In the first part, under feeble magnetic force, the slope of the curve is very small; later, in the second part, as the force increases, the curve becomes very steep; in the third part the slope of the curve remains fairly constant; and finally in the fourth part, the curve rounds off and the rate of ascent again becomes very small. The _susceptibility_ for induced magnetisation is thus very feeble at the beginning; under increasing force, in the second stage, the susceptibility becomes greatly enhanced; in the third stage, the susceptibility remains approximately constant; and in the fourth stage it becomes diminished. We shall presently find that the susceptibility for excitation also undergoes a similar variation at the four different stages of stimulation.

CHARACTERISTICS OF SIMPLE PHOTOTROPIC CURVE.

I have shown (Fig. 130) the relation between the stimulus and the resulting excitation, the latter being determined from the diminution of the rate of growth. Under unilateral action of light, the excitatory contraction gives rise to tropic curvature. We may thus obtain the characteristic excitation curve, by making the plant organ record its tropic movement under continuous action of light applied on one side of the organ.

[Ill.u.s.tration: FIG. 131.--Characteristic curve of iron under increasing magnetising force. (After Ewing).]

[Ill.u.s.tration: FIG. 132.--Simple characteristic curve of phototropic reaction. Excitation increases slowly in the first part and rapidly in the second; it is uniform in the third, and undergoes decline in the fourth part (_Erythrina indica_).]

_Experiment 134._--I give below the characteristic curve of excitation (Fig. 132) of the pulvinus of _Erythrina indica_, traced by the plant itself, and exactly reproduced by photomechanical process. A parallel beam of light from a Nernst lamp was thrown on the upper leaf of the pulvinus, and the increasing positive curvature was recorded on a smoked gla.s.s plate which was moved at an uniform rate. The successive dots are at intervals of 20 seconds; the horizontal distances between successive dots are equal, and represent equal increments of stimulus; the vertical distances between successive dots represent the corresponding increments of excitation. The gradient at any point of the curve--increment of excitation divided by increment of stimulus--gives the susceptibility for excitation at that point. The following table will show how the susceptibility for excitation undergoes variation through the entire range of stimulus. The average susceptibility for each point has been calculated from the data furnished by the curve.