In the preceding chapters we discussed the various factors which characterize ameboid movement: the streaming of the endoplasm, the formation of ectoplasm, and the behavior of the surface film. The discussion has involved only momentary cross-sections of the life of an ameba, following the method of investigation in general use for the solving of problems connected with ameboid movement. It has been tacitly assumed that if one could explain ameboid movement at any particular cross-section in time, one understood the whole process of ameboid movement no matter how long it continued, excepting, of course, the action of various kinds of stimuli that produced changes in direction, speed, etc., of streaming. It was not assumed that time was an element in the practical sense in the explanation of locomotion. A few seconds’ or a few minutes’ comprehensive observation was supposed to furnish sufficient basis for an explanation.

Sometime ago I discovered however that the path of an ameba as it moves over a flat surface free from particles possesses character; it is not an aimless irregular zigzagging here and there, such as has been generally supposed, and in occasional instances asserted, to be the case. On the contrary, the path of an ameba during the course of an hour or two consists of a succession of gentle right and left-hand curves alternating with each other. The general appearance of the path is that of a flattened spiral. Having observed a part of an ameba’s path, therefore, one can predict with considerable accuracy in what direction the ameba will continue to move. Thus that scientific bugaboo “Random Movement” is evicted from that strongest of his strongholds, the aimless wanderings of the ameba.

The mechanism producing the sinuosities in the path of the amebas is easily disturbed by external or internal stimulation of various sorts, resembling in this respect the spiral path of a paramecium, which is also easily changed by the presence of various solid and dissolved substances in the culture medium. But the mechanism controlling the direction of the path of an ameba is apparently much more delicate than that in paramecium, for it is only occasionally that a considerable succession of regular sinuosities are described by an ameba in moving over a flat surface. On the other hand, a few fair curves are found in the path of practically every ameba if carefully observed for an hour or more under favorable conditions.

To observe the path an ameba describes in moving over a flat surface, the following conditions must be fulfilled. One must have a small glass dish with a flat bottom, polished preferably, but not necessarily, of the size of a small petri dish, but square so as to fit into a mechanical stage. The dish should be filled with culture fluid free from solid particles. Centrifuging the culture medium, or dialyzing distilled water in the culture medium, will yield a satisfactory medium. It is only by experience that one can pick out an ameba that seems to be in an optimum condition for this purpose, that is, free from strong internal stimuli, such as those from a large mass of food, etc. Just as we speak of “clean-limbed” athletes, meaning thereby a high degree of muscular coÖrdination, so one who has worked with these animals for some time acquires the capacity to pick out “clean-limbed” amebas; though how these differ from others is just as impossible to describe adequately as to tell what a clean-limbed athlete is. But having selected two or three amebas that move in a well coÖrdinated manner and passed them through two or three changes of water free from particles, they are placed in the middle of a dish and allowed to remain for ten or fifteen minutes before observations are begun. A small shade should be placed in front of the dish if very strong light can reach it. It does not matter if diffuse light reaches the dish. A camera lucida with its appurtenances is absolutely essential. In addition to the ordinary precautions the edge of the paper must be laid parallel with the side of the mechanical stage, for a number of sheets of paper will have to be used up in the course of an hour or two and these must be pasted together properly to reconstruct the path. The best magnification shows the ameba two to five cm. long on the paper. Drawings should be made quickly but carefully, beginning and ending with the posterior end of the ameba.

One of the best examples of the sinuous path of an ameba is shown in Figure 33. It is the path of an Amoeba bigemma from a natural out-door culture. The observations were made under the conditions outlined above. The temperature, which is an important factor, was unfortunately not recorded, but it was about 28° C.

Practically the whole of the path of this ameba consists of right and left-hand curves which are nearly uniform in length, each wave being about eight to ten times the length of the ameba. Since the drawings were made at intervals of a minute, the waves are therefore from eight to ten minutes long in time, measuring from crest to crest. Some of the waves are flatter than others, for example wave No. 4, but otherwise it is like the others. Wave 7 is a double wave due to a change of direction. Instead of turning to the right at 9:23 the ameba changed its direction and turned to the left. The smoothness with which this turn was made indicates that it originated in the mechanism producing the sinuous course itself, or that it proceeded from a very slight stimulus external to it. At 9:49 the direction of movement was changed again, but just enough to disturb the formation of a smooth wave. The general direction of locomotion was not changed. It may be assumed that this change was produced by a stimulus external to the wave-producing mechanism. The irregularity and shortness of wave 13 was probably due to the same stimulus that disturbed wave 11. Shortly after 9:58 the ameba came within sensing range of a mass of debris which it pushed away and followed, thus causing a change in the direction of movement. Although waves begin to appear again after this, some of them very smooth, they are not typical for they are too short, ranging from a little over three lengths (wave 16) to a little over six lengths (wave 23). It is likely that the disturbance caused by the mass of debris at 9:58 together with the onset of the division crisis produced the succession of atypical waves. An external disturbance that is sufficiently strong to change the direction of locomotion usually persists for the duration of at least one wave length thereafter. It will be noted that

the approach of the division crisis did not tend to destroy the action of the wave mechanism, but only slowed down movement and shortened the waves. The path of one of the daughter amebas was followed for a short time, in which there is evidence of a wavy path, but it soon came upon a small mass of debris which it ingested and soon thereafter reversed its direction of movement. This behavior made it unprofitable to continue further observation of this ameba. For the gradual change in direction to the left from wave 1 to 6 in the path of the parent ameba, no adequate explanation has suggested itself.

That amebas react to light has been shown by Verworn (’89), Davenport (’97), Harrington and Leaming (’00), Mast (’10) and especially Schaeffer (’17). It appeared desirable therefore to control the rays of light, for it was thought possible that light might be a factor in the formation of the wavy path. Since no method has yet been devised that permits of the observation of the path of the ameba other than a succession of camera lucida outlines, it is impossible to omit light altogether in the experiments. The next best procedure was therefore followed, viz., the alternation of periods of darkness of a few minutes’ duration with brief—ten-second—periods of light, to permit the drawing of camera lucida outlines. The dish in which the amebas were observed was placed in a light-tight box and all light excluded except that which passed through “Daylite” glass with an opal surface on both sides between the condenser and the light source. None but parallel beams, passed through a condenser, reached the ameba. The metal parts of the objective were also blackened. The work was done in a dark room.

Figures 34 and 35 show sections of the path of two Amoeba discoides under these experimental conditions. The amebas were for the most part in clavate shape, which is the most favorable shape for the formation of smooth waves. In figure 34, from 2:29¼ to 2:42¼ the ameba was in continuous light. A section of a little more than one wave is shown. Although pseudopods were thrown out at considerable distances to the right and left of the path, a smooth, wavy path was nevertheless maintained. At 2:42½ the light was turned off until 2:58½ except for two ten-second flashes at 2:47 and 2:52. During the first period of

darkness the ameba merely kept on in the direction it was going when the light was turned off. But during the second period of darkness the ameba changed its course in such a way as to make a smooth curve. In the third period of darkness the ameba continued on its course completing the wave. It is thus apparent that continuous light is not necessary to the formation of waves nor is it detrimental to their formation. Figure 35 shows essentially the same thing as Figure 34. The light was turned on from 3:30½ to 3:32. During this time the behavior of the ameba was irregular, but whether this was caused by the light or not, cannot be stated. At 3:43 the ameba came into contact with a small particle which changed its course. The slow speed of movement of these two amebas was due to the low temperature (20° C.), the experiments being performed in January. The apparent connection between longer waves and darkness has not yet been investigated.

Figure 36 shows the path of an Amoeba proteus under controlled light conditions as above described, but instead of moving over a polished plate glass surface as in the previous experiments, the ameba in this experiment moved over a fine ground-glass surface. It will be observed that for the first twenty minutes the path shows smooth waves, although at 11:53 and 11:55 there was a slight disturbance which was associated with the formation of numerous pseudopods. From 12:07 on, however, the path becomes irregular, the wave-like character being almost obliterated. Associated with this irregularity is the presence of numerous pseudopods. This is a sample of a number of records which indicates that in proteus and discoides the presence of numerous pseudopods in some way prevents the ameba from moving in a path marked by smooth and conspicuous waves.

When a wave in the path for some reason becomes unusually long, there is likely to be a very abrupt and decided change in the direction of movement, which is away from the convex side of the wave. Figure 37 is inserted here to illustrate this point. The ameba should have turned to the left at 3:43 to keep the waves of typical size, and at 3:45 a pseudopod was extended in this direction a short distance, but again the curve toward the right persisted. But at 3:48½ the ameba broke up into several pseudopods at right angles with the main axis, and through one

of these the ameba moved on with the reestablishment of the wavy path. The tendency to wave formation evidently has to overcome resistance of some sort.

Although amebas in clavate shapes describe the smoothest waves in their paths, waves may also be detected in the paths of amebas that habitually form many pseudopods. The path of an Amoeba dubia is shown in Figure 38. The ameba moved on an opal surface under light-controlled conditions. If we had not already seen how proteus, discoides, and especially bigemma formed smooth waves in their paths, we should hardly be able to understand the apparently aimless path of dubia. But having seen how a regular succession of smooth waves appears under favorable conditions in the paths of these amebas, there can be little question but that the staggering path of a dubia also is to be interpreted as a succession of waves, although they are somewhat irregular.

These four species of amebas, proteus, dubia, discoides and bigemma are the only species that have been specially investigated as to their paths, and they all show such paths, as we have seen. The presumption is strong therefore that it is a common characteristic of amebas.

To learn something of the nature of the wave-forming mechanism in the ameba, it is necessary to find some agencies that modify the activity of this mechanism. That there are such factors is of course evident enough from what has been said already about wavy paths, and from the appearance of the paths themselves. But the factors which influence the formation of waves in so far as they may be known or reasonably suspected, are internal and therefore difficult to make use of experimentally.

One of the most readily applied stimuli that is known to affect the character of ameboid movement is temperature. In general, the lower the temperature, the slower the movement. This has frequently been observed and recorded. Such behavior is to be expected from a viscous fluid like protoplasm. This may therefore be a purely physical phenomenon. But the lowering of the temperature has also another effect on the movement of amebas: it creates in them a tendency to cross their paths more frequently. Figure 33 is a typical example of the path of an ameba in a high temperature (28° C.). It did not cross its path at all during the hour and a half it was under observation. When the temperature is low (20° C.) the path becomes contracted and the ameba seems unable to get away from the place it happens to be in. Movement of course continues but it is slower, and a large number of loops occur in the path. Figure 39 indicates the general path of an ameba under controlled conditions in a temperature a little lower than room temperature, that is, about 20° C. During the four hours that it was under observation the ameba crossed its path eight times and made a number of very short turns besides. Leaving out of account the loops in the path there are a number of sections which may be interpreted as waves, such as for example the pronounced waves a short distance from the end of the path. All these waves are shorter but much deeper than the waves made in a higher temperature. The loops in the path (all excepting the first, which is a compound loop) represent each a single wave which have become so deep and contracted that they have become transformed into circles. As the temperature decreases, the crests of the waves rise higher and higher, and the bases contract more and more, until the two sides of the waves come together, resulting in the formation of circles (Figure 40). The actual size of the wave also decreases at the same time from about eight times the length until it is only two or three times the length of the ameba. Temperature affects therefore the wave mechanism independently of the mere viscosity of the endoplasm. The speed of movement is not merely slowed down, but the character of the waves themselves is changed.

Amebas sometimes react to stimuli by moving around the source of the stimulus at a more or less uniform distance through one or more quadrants of a circle, instead of reacting positively, negatively, or indifferently, in a definite manner, to the source of the stimulus (Schaeffer ’16, ’17). See Figure 41. The explanation that has been given by this investigator is that the encircling is due to a balance between the tendency to move ahead in the original direction (“Functional inertia”) and a tendency to react positively. But now that we know that amebas tend to form waves in their paths, the explanation of encircling becomes simpler and perhaps also more convincing.

In the first place, instances of encircling are relatively rare in the reaction of amebas, much rarer than one would expect if it depended merely upon a balance between two tendencies, one to move ahead and the other to move toward the source of the stimulus. Any explanation of this phenomenon has therefore to account for the rarity with which it occurs as well as the operation of the phenomenon itself. This the explanation based upon the position of the source of the stimulus with reference to the configuration of the wavy path can do satisfactorily.

In the experiments with temperature it was found that when the temperature is 20° C. or lower, the waves tend to curl up, to become transformed into circles. That is, the base of one

wave, instead of running into the base of the next wave is reflected backwards to form a circular curve. All the evidence thus indicates that the weakest point is at the base of the wave. A constantly acting stimulus may therefore break the wave here if it cannot break into it elsewhere, and so change the direction of the path. In Figure 42 are shown a few diagramatic waves in the path of an ameba together with several reflected curves at 1, 2 and 3 indicating the points at which the direction is most easily changed as evidenced by the temperature experiments. If a particle within sensing range of the ameba lie at a, b, or c, and stimulate the ameba only slightly but still enough to break up the wave formation, the ameba will take a curved path around the particle as indicated by the dotted lines. But if the same particle lay at any other point with reference to the position of the wave, as at e, f, or g, the ameba would not have changed its course. Briefly, the following conditions must be satisfied to enable the phenomenon of encircling to appear: (1) The particle must lie a little to the side of the ameba’s path. (2) It must lie abreast of the point at which the ameba begins to change its direction of movement (i. e., at the base of the wave) when describing

waves. (3) It must stimulate the ameba just strong enough positively to break into the wave-forming process. Encircling then is due to a “balance” between a positive stimulus and a tendency to move in a curve. This explanation conforms with all the data at hand and explains also the rarity of the phenomenon, for the chances of encircling occurring on this view are rather less than one-fifth as frequent as if encircling took place whenever a balance between a tendency to react positively and to move straight ahead occurred.

That the wavy path is broken up by the receipt of a stimulus, that is, by a true sensation, rather than by direct effect of some agency radiating from the particle, is indicated by the fact that stimuli proceeding from various substances, such as keratin, glass, carbon, light beams, etc., have all the same effect.

In attempting to explain the characteristic nature of the path of the ameba, one’s attention centers first, perhaps, upon its orderliness; a result undoubtedly of the general impression propagated through hastily written textbooks and general papers, that an ameba’s whole life is a direct response to its environment. As the recorded facts of the life of this organism are accumulating, it is coming to be seen that the ameba possesses all the fundamental attributes of animals generally, in addition to many special ones. So that as a matter of fact, if the ameba did not show some character and orderliness in its locomotion, then for the first time should we be especially interested in what would have to be regarded as a very striking and exceptional characteristic.

For it is very well known, and it is generally recognized by everybody, that moving organisms usually move in an orderly manner; it is recognized that organisms tend to move in straight paths excepting where interrupted by the action of some special stimulus. When an organism changes its direction of motion frequently and abruptly, we call it erratic. The mad dashings-about of the hunter-cilitae Didinium and the unceasing gyrations of the whirligig beetle excite one’s curiosity because these organisms do not move as other organisms do; they contradict our expectation of movement in a straight line.

But why should organisms generally tend to move in straight paths? This fundamentally important question has received almost no attention, excepting that rapidly moving animals like birds, flying insects, fishes and other rapidly swimming animals of various kinds and rapidly running animals tend to move in straight paths because of the physical inertia of the mass of the organism. It is easier for a rapidly moving organism to move in a straight line than to change its direction of movement frequently and abruptly.

The ameba however is a very slow moving animal, as animals go, for it (proteus) moves only about 600 microns per minute. Under the microscope, however, which magnifies speed as well as size, the endoplasmic particles rush along rapidly enough to suggest that even here mere physical inertia might be a determining factor in the path of the ameba, which for considerable segments is often very nearly straight. Such suspicion is not justified, however, for the viscosity of the endoplasm taken in connection with the heterogeneous composition of the ameba, makes it improbable that mere physical inertia can affect the path of the ameba.[5]

It is not even necessary that movement of the endoplasmic stream be interrupted in order that a straight path may be maintained. An ameba may stop movement for a minute or more and then be much more apt to resume movement in the original direction than in any other. This is brought out by the following series of experiments.

Of sixty cases of feeding on various kinds of particles, by as many different amebas, in which the direction of movement before and after a particle was eaten was recorded, thirty-nine moved off in the same direction after eating as before eating. By moving off in the same direction is meant that the ameba did not move more than 22½° to the right or to the left of the direction of movement before feeding. The circle was thus divided into octants, and the expectation of movement in the same direction after eating a particle, if it were a matter of chance, would have been seven and one-half cases instead of thirty-nine.

But it is not only the process of feeding that has to be considered in this connection, for feeding occasionally is affected by a side pseudopod while the main body of the ameba moves on without being visibly affected as to its direction of movement. No such case is included in the figures just given. In each of these sixty cases the endoplasmic streams of locomotion were completely stopped, from about twenty seconds to seventeen minutes. In most cases the endoplasmic stream was also completely disorganized, the ameba assuming a nearly spherical form in which more or less well marked though small cross currents of endoplasm could be detected. The direction of the light was without effect, for the paths extended in every direction with respect to the light both before and after feeding. Further, it has been shown that ordinary diffuse light is without effect on the movements of the ameba (Schaeffer, ’17). It may be concluded therefore that the ameba tends to keep on moving in straight paths even if the highly disorganizing act of feeding and the consequent resting period of a few seconds to many minutes supervenes at some point in its path. To what this induction of the original path is due is not clear, thought it is possible that the physical condition of the ectoplasm at the anterior end is different from that elsewhere and that it requires less energy in consequence, or for some other reason, to flow in the original direction. This explanation is based on the observation that it is easier for the ameba to activate the remnants of old pseudopods than to form new ones (Schaeffer, ’17).