Among the more aberrant forms of Infusoria is a little species known as _Trichodina pedicidus_, a parasite on the Hydra, or fresh-water polype (Fig. 81.) This Trichodina has the form of a more or less flattened circular disc, with a ring of cilia around both its upper and lower margins. The salient ridge from which these cilia spring may be taken, as we have already said, to play the part of a strengthening “fillet.” The circular base of the animal is flattened, in contact with the flattened surface of the Hydra over which it creeps, and the opposite, upper surface may be flattened nearly to a plane, or may at other times appear slightly convex or slightly concave. The sides of the little organism are contracted, forming a symmetrical equatorial groove between the upper and lower discs; and, on account of the minute size of the animal and its constant movements, we cannot submit the curvature of this concavity to measurement, nor recognise by the eye its exact contour. But it is evident that the conditions are precisely similar to those described on p. 223, where we were considering the conditions of stability of the catenoid. And it is further evident that, when the upper disc is actually plane, the equatorial groove is strictly a catenoid surface of revolution; and when on the other hand it is depressed, then the equatorial groove will tend to assume the form of a nodoidal surface. Another curious type is the flattened spiral of _Dinenympha_[302] {253} which reminds us of the cylindrical spiral of a Spirillum among the bacteria. In Dinenympha we have a symmetrical figure, whose two opposite surfaces each constitute a surface of constant mean curvature; it is evidently a figure of equilibrium under certain special conditions of restraint. The cylindrical coil of the Spirillum, on the other hand, is a surface of constant mean curvature, and therefore of equilibrium, as truly, and in the same sense, as the cylinder itself. [Illustration: Fig. 82. _Dinenympha gracilis_, Leidy.] [Illustration: Fig. 83.]