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 hours0.0001726.325 seconds1.099827.5
13  "0.00043920.68  "3.0281324.2
10  "0.00060921.94  "5.45621.8
6  "0.00085518.62  "8.45316.9
3  "0.00176919.11  "18.9418.9
100 minutes0.00270616.225  "45.0518.0
60  "0.00477317.2225  "308.724.7
30  "0.0101818.3125  "511.420.5
20  "0.0164019.7155  "125522.8
15  "0.024922.41100  "190219.0
8  "0.049823.91400  "790519.8
4  "0.089821.61800  "1309416.4
40 seconds0.615624.811000  "2652026.5

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