Note 5 — Chapter XII · The Wavy Path of the Ameba

According to Ewart (’03) the viscosity of streaming protoplasm in plant cells lies between η = .04 and η = .2. But the velocity of streaming endoplasm in ameba is considerably slower than that in the plant cells which formed the basis for Ewart’s calculations. In comparison, we may estimate the viscosity of the endoplasm of ameba as η = .1 dynes per sq. cm. The velocity of streaming endoplasm, as ascertained by observations on Amoeba dubia (in which the endoplasm flows usually rapidly) is 1/880 cm. per second.

Now, given a unit mass of endoplasm moving at a given instant with a 1 velocity of ¹/₈₈₀ cm. per second against viscosity of η = .1 dynes per sq. how far will the unit mass travel before coming to rest?

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.