III. CENTROPLANE TYPES.--The natural middle of the body is a plane, the median or chief plane (_planum medianum_ or _sagittale_); it divides the bilateral body into two symmetrical halves, the right and the left. With this is associated the characteristic antithesis of back (_dorsum_) and belly (_venter_); hence, in botany this type (found, for instance, in most green leaves) is called the dorsiventral, and in zoology the bilateral in the narrower sense. One characteristic of this important and wide-spread type is the relation of three different axes, vertical to each other; of these three straight axes (enthyni) two are unequipolar and the third equipolar. Hence, the centroplanes may also be called tri-axial (_triaxonia_). In most of the higher animals (as in our own frame) the longest of the three axes is the principal one (_axon principalis_); its fore pole is the oral or mouth pole, and its hinder pole is the aboral or caudal (tail) pole. The shortest of the three enthyni is, in our body, the sagittal (arrow) or dorsiventral axis; its upper pole is at the back and its lower pole at the belly. The third axis--the transverse or lateral axis--is equipolar, one pole being called the right and the other the left. The various parts which make up the two halves of the body have relatively the same disposition in each half; but absolutely speaking (namely, in relation to the middle plane) they are oppositely arranged. Further, the centroplane or bilateral forms are also characterized by three vertical axes which may be drawn through each of the normal axes. The first of these normal planes is the median plane; it is defined by the chief axis and the sagittal axis, and divides the body into two symmetrical halves, the right and left. The second normal plane is the frontal plane; this passes through the chief axis and the transverse axis (which is parallel to the frontal surface in our body), and divides the dorsal half from the ventral half. The third normal plane is the cingular (waist) plane: this is defined by the sagittal and transverse axes. It divides the head half (or the vertical part) from the tail half (or the basal part). The name "bilateral symmetry," which is especially applied to the centroplane and dorsiventral types, is ambiguous, as I pointed out in 1866 in an exhaustive analysis and criticism of these fundamental forms in the fourth book of the _General Morphology_. It is used in five different senses. For our present general purpose it suffices to distinguish two orders of centroplane types, the bilateral-radial and the bilateral-symmetrical; in the former the radial (pyramidal) form is combined with the bilateral, but not in the latter.