Force = Mass × Acceleration, and Acceleration = Velocity/Time.
η = Viscosity = F = MA = MV/T.
Now if M = 1, η = F = A = V/T.
T = V/η = 1/880/.1 = 1/88.
The space travelled over in uniformly accelerated motion equals
S = 1/2 AT² = 1/2 × 1/10 × (1/88)² = 1/154880 = .00000645 cm.
If, therefore, the force moving the central stream of endoplasm should suddenly be discontinued, the resistance offered by the viscosity of the enveloping endoplasm would allow it to move only .0000645 mm. before coming to rest. But the ameba as a whole moves more slowly than the central stream of endoplasm, the average rate of movement being about 1/300 mm. per second. The effect of the streaming endoplasm on the forward movement of the whole ameba would therefore be correspondingly decreased. Now if the ameba was perfectly homogeneous and perfectly symmetrical, and free from external stimulation, and moved in a perfectly homogeneous liquid on a perfectly plane surface, the excessively small amount of mechanical inertia would then be sufficient, theoretically, to cause the ameba to move in a straight instead of an irregular path. But these conditions are never realized. The ameba is unsymmetrical in form, heterogeneous in composition and always unsymmetrically stimulated; hence it is impossible that the excessively small amount of mechanical inertia can be considered a factor in determining the direction of the ameba’s path.
[6] The gap between the rate of movement of a pseudopod and that of a flagellum is however very wide. Insofar as the character of the movement is concerned, pseudopods such as those of flagellipodia, probably resemble the flagella of the soil ameba and of flagellates. But the very much greater speed of contraction of a flagellum and the presence of a special organ (blepharoplast) at the base of the flagellum, and their connection with the nucleus, indicates that a special mechanism is necessary to cause the rapid contraction. A flagellum appears to be a pseudopod supplied with something like nerve tissue and a ganglion capable of setting free a rapid succession of impulses.
[7] It should be added here that since this paragraph was written I have been very fortunate to secure numerous records of paths swam by blindfolded swimmers, which strikingly resemble those of persons walking blindfolded as described above. Most of the common swimming strokes were employed in these observations and occasionally several strokes were employed in a single experiment. In a few cases the spiral path was made up of over twenty turns, and in one case of over fifty turns. A fuller discussion of these results does not seem pertinent here, and must be deferred to a later date.
[8] Since this was written I have been able to examine the movement of live sperm cells in a number of representative animals, including the jellyfish Aurelia; the molluscs Ostrea, Solemya, Pandora; the arthropods Limulus and Anisolabia, and the vertebrates frog, turtle, snake, cat, dog and man, with the result that all these spermatozoa revolve on their long axes and swim in spiral paths resembling those of flagellates. Owing to their minute size their movements are made out only with great difficulty, but so far as could be determined all the sperms of any one species turn on their axes in the same way, that is, either right-handed or left-handed. Recently there has also come to my notice the very informing paper of W. D. Hoyt, 1910, in the Botanical Gazette, in which it is stated that fern sperms of various species swim in spiral paths.