With time, however, the oppo sition to this theory has been greatly increased, and there are many naturalists who have almost completely relinquished it. Fre quently, the law which governs the movements of such animals is known by another name, namely the "Law of Resultants." Thus, if we allow an animal to crawl into a field of light which is formed by two crossing beams, it is compelled to move according to the resultant. A fine example of this manner of reaction has been furnished by Frl. Muller, who worked with woodlice (see fig. 15). It ap pears that the animals under the influence of two equally strong beams of light, run exactly in the diagonal; if the beams are made to be of unequal strength the angle alters. It can be calculated in advance if we know the strength of both beams of light.
A second theory, which is in opposition to the theory of trop isms, asserts that the lower animals behave similarly to man and the higher animals. If a man walks towards a light, or let us say in a general way towards some optically perceptible point, first of all he fixes his eyes on the light, that is to say he moves . them so that the light falls on thecentral point (fovea centralis), he then turns his head and body towards the light and goes straight forward. Kuehn has named this kind of reaction "telo taxis"; it is fundamentally op posed to tropotaxis, as will ap pear if we close one eye. A telo tactically reacting animal is just as well able to direct its course when using only one eye as when using both; a tropotactically re acting animal, on the other hand, when it has only one eye is com pelled continually to move round in circles. It is easy to convince oneself, on the basis of this alter native, that the majority of the more highly developed animals, such as insects or the higher groups of Crustacea, behave for the most part telotactically.
The numerous partial refutations which the theory of tropisms has undergone cannot be given in detail here. Only one particu larly important argument can be mentioned. It used to be con sidered a proof of its validity that animals blind on one side constantly run round in circles. If they are positively photo tactic, they continually turn towards the side on which they can see; if they are negatively phototactic they turn towards the blind side. Now, in the first place, this certainly does not apply to all cases. The majority of the higher insects learn very quickly to run straight when they have only one eye. Above all, Mast was able to prove that the animal does not move round in circles involuntarily, as the theory of tropisms would require, but that the animal voluntarily runs round thus, and moves its legs in such a manner as to attain this end. If some of the legs are amputated the remaining ones completely alter their move ments, so that, in spite of the totally different locomotor con ditions, the circus movement is still possible.
A second argument of general application is as follows:—The naturalist usually makes use of horizontal light in his experi ments, which strikes the animal from one side. Only under these artificial conditions is it possible to turn about an axis which lies in the plane of symmetry of the body. Under natural con ditions, on the contrary, the light, as far as aquatic animals are concerned, comes always from above. The Daphnia on becoming positively phototactic turns from its former position, not to right or left, but backwards. That it swims in the end towards the light, and not in the direction A or B is impossible to understand on the theory of tropisms (fig. i6).
Frequently, however, it is impossible to decide with certainty from such rough experiments the manner in which an animal orientates itself in relation to light, and a closer, more exact analysis is required. We are indebted to S. 0. Mast for the best work on this subject. He showed that in many cases, neither tropotaxis nor telotaxis sufficed to account for the phenomena. As the first example we may mention briefly the researches of Mast on the orientation of the colonial Flagellate, Vo/vox. The colony is composed of about 20,000 individuals, which are ar ranged on the surface. Each zooid has two flagella, and an eye spot, provided with a lens. The colony has an anterior pole, which is always turned towards the front in swimming, and a longitudinal axis round which it rotates. If a light is placed to one side of a positively phototactic colony, it turns until the anterior pole is directed to the light, and then swims straight towards it. This gives the impression of being a clear case of tropotaxis, but Mast was able to prove that the zooids on the illuminated and on the shaded sides differ, not in the strength of the lashing of the flagella, but in the direction of the strokes. On the former side the flagella lash sideways, on the latter, straight out to the back (see fig. 17). It is apparent, theref ore, that in this reaction we are dealing neither with a case of tropo taxis nor with one of telotaxis, but with a phenomenon sui generis. Very interesting are the orientation movements of asymmetrical animals, as for example one-eyed animals such as the Ascidian larvae also studied by Mast. These animals are negatively phototactic, and in swimming revolve about their longitudinal axis. When the light comes from one side, the eye, which is set in a pigmented cup, is alternately illuminated and in shadow with each revolution. Every time it is in shadow, the animal makes a stroke with its tail towards the ocular side ; every time it is illuminated, it makes a stroke towards the abocular side (see fig. 18). In this way the larva quickly turns away from the light.