It is very difficult to prove directly the applicability of the Bunsen-Roscoe law for free-moving animals, but it can be shown that intermittent light is as effective as constant light of the same intensity, provided that the total duration of the illumination by the intermittent light is equal to that of the constant light, and the duration of the intermission is sufficiently small (Talbot’s law). Talbot’s law is in reality only a modification of the Bunsen-Roscoe law. Ewald has proved in a very elegant way the applicability of Talbot’s law to the orientation of the eyestalk of Daphnia.[224] This makes it probable that the law of Bunsen-Roscoe underlies generally the heliotropic reaction of animals.
It is of importance for the theory of the identity of the heliotropism of animals and plants that in the latter organisms the law of Bunsen and Roscoe is also applicable. This had been shown previously by Fröschel[225] and by Blaauw.[226] In the following table are given the results of Blaauw’s experiments on the applicability of the Bunsen-Roscoe law for the heliotropic curvature of the seedlings of oats (Avena sativa). The time required to cause heliotropic curvatures for intensities of light varying from 0.00017 to 26520 metre-candles was measured. The product i t, namely metre-candles-seconds, varies very little (between 16 and 26).
TABLE VII
| I Duration of Illumination | II Metre-Candles | III Metre-Candles-Seconds | I Duration of Illumination | II Metre-Candles | III Metre-Candles-Seconds | |||
|---|---|---|---|---|---|---|---|---|
| 43 | hours | 0.00017 | 26.3 | 25 | seconds | 1 | .0998 | 27.5 |
| 13 | " | 0.000439 | 20.6 | 8 | " | 3 | .02813 | 24.2 |
| 10 | " | 0.000609 | 21.9 | 4 | " | 5 | .456 | 21.8 |
| 6 | " | 0.000855 | 18.6 | 2 | " | 8 | .453 | 16.9 |
| 3 | " | 0.001769 | 19.1 | 1 | " | 18 | .94 | 18.9 |
| 100 | minutes | 0.002706 | 16.2 | 2⁄5 | " | 45 | .05 | 18.0 |
| 60 | " | 0.004773 | 17.2 | 2⁄25 | " | 308 | .7 | 24.7 |
| 30 | " | 0.01018 | 18.3 | 1⁄25 | " | 511 | .4 | 20.5 |
| 20 | " | 0.01640 | 19.7 | 1⁄55 | " | 1255 | 22.8 | |
| 15 | " | 0.0249 | 22.4 | 1⁄100 | " | 1902 | 19.0 | |
| 8 | " | 0.0498 | 23.9 | 1⁄400 | " | 7905 | 19.8 | |
| 4 | " | 0.0898 | 21.6 | 1⁄800 | " | 13094 | 16.4 | |
| 40 | seconds | 0.6156 | 24.8 | 1⁄1000 | " | 26520 | 26.5 | |
It is, therefore, obvious that the blind instinct which forces animals to go to the light, e. g., in the case of the moth, is identical with the instinct which makes a plant bend to the light and is a special case of the same law of Bunsen and Roscoe which also explains the photochemical effects in inanimate nature; or in other words, the will or tendency of an animal to move towards the light can be expressed in terms of the Bunsen-Roscoe law of photochemical reactions.
The writer had shown in his early publications on light effects that aside from the heliotropic reaction of animals, which as we now know depends upon the product of the intensity and duration of illumination, there is a second reaction which depends upon the sudden changes in the intensity of illumination. These latter therefore obey a law of the form: Effect = f (di/dt).[227] Jennings has maintained that the heliotropic reactions of unicellular organisms are all of this kind, but investigations by Torrey and by Bancroft[228] on Euglena have shown that Jennings’s statements were based on incomplete observations.
4. In these experiments only one source of light was applied. “When two sources of light of equal intensity and distance act simultaneously upon a heliotropic animal, the latter puts its median plane at right angles to the line connecting the two sources of light.”[229] This fact has been amply verified by Bohn, by Parker and his pupils, and especially by Bradley Patten, who used it to compare the relative efficiency of two different lights.
The behaviour of the animals under the influence of two lights is a confirmation of our theory of heliotropism inasmuch as the animal moves in such a direction that the symmetrical elements of the surface of the body are struck by light of the same intensity at the same angle, so that as a consequence equal masses of photosensitive substances are produced in symmetrical elements of their eyes or skin in equal times. The effect on the symmetrical muscles will be identical. As soon as one of the lights is a little stronger the animal will deviate towards this light, in case it is positively heliotropic and towards the weaker light if it is negatively heliotropic. This deviation again is not the product of chance but follows a definite law as Patten[230] has recently shown. He used the negatively heliotropic larvæ of the blowfly. These larvæ were made to record their trail while moving under the influence of the two lights. The results of the measurements of 2500 trails showing the progressive increase in angular deviation of the larvæ (from the perpendicular upon the line connecting the two lights), with increasing differences between the lights, are given in the following table. Since the deviation or angular deflection of the larvæ is towards the weaker of the two lights it is marked negative.
TABLE VIII