Some organisms possess body shapes that seem to be due to the habit of spiral swimming. Jennings (’01) describes a species of rotifer whose body forms a segment of a spiral. When swimming a spiral path is described, “of which its own twisted body forms a part” (p. 376). Elsewhere he has pointed out that the oral groove of a paramecium likewise coincides with its own spiral path. Indications of such correspondence between the axis of a structure and the spiral path the organism possessing it, describes, are numerous among free swimming animals. But such correspondence (with an imaginary spiral path) is also found in organisms that do not swim freely. One of the most interesting of such cases is found in the _Oscillatoriaceae_. In a previous chapter it was seen that many of these organisms are capable of moving about by means of a film of what is probably protoplasm, which moves spirally around the filament. A particle attached to this film describes a spiral path like that of a flagellate or a ciliate. Most of the _Oscillatoriaceae_ that are capable of movement, consist of straight filaments; but two of the genera, _Arthrospira_ and _Spirulina_, are spirally twisted in such a way that the spiral axis of the filament corresponds approximately to the spiral path of a particle attached to the surface film of an _Oscillatoria_ filament, except, of course, in size. (The movement of the surface film of neither _Arthrospira_ nor _Spirulina_ has been studied). That the spiral shape of a rotifer, for example, may be caused by swimming in a spiral path might perhaps be regarded as a plausible explanation, but it seems to me that it would be more satisfactory to explain the spiral shape of rotifers and _Arthrospira_, the direction of the oral groove of paramecium and similar structures in other organisms, as due to the same fundamental process that causes the spiral path in locomotion. This explanation is purely mechanistic and avoids the teleological element on which the other explanation ultimately depends.