1. The negative phototropism of certain land isopods was investigated over a large range of intensities, especially low ones. The responses were determined quantitatively by measuring the angle through which an animal turned away from a line perpendicular to the rays of light.

2. In the absence of light the undirected movements set up by obscure stimuli were such as to compensate each other statistically, the average path being a movement in the direction in which the animal was headed.

3. Over a large range of intensities (0.0026 m.c. up) the average turning is maximal, about 55° (Oniscus). This maximal response is due to an anatomical peculiarity, in that the carapace cuts off the light on the eye after the animal has turned 50–60°. This peculiarity probably accounts for specific differences among land isopods. Any light, therefore, which is strong enough to turn an animal through this maximal angle in a radial distance of 10 cm. will give results whose mean will be maximal.

4. Below 0.0026 m.c. the amount of angular deflection becomes less and less, in proportion to the logarithm of the intensity, until at 0.00003 m.c. the movements are the same as in darkness.

5. This proportionality between amount of turning and the logarithm of the intensity indicates the photochemical nature of phototropism on the basis of Hecht's work with Mya. As a result, Loeb's theory of phototropism may then be stated in the mathematical form

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in which I1 and I2 are the two intensities, E1 and E2, their respective effects, and R, the muscular action set up by the difference in photochemical effect on the two sides.

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