The considerations which apply to this example will be found operating in many cases of the variation of terminal members of linear series. Some of these series, like the teeth of the dog, end in a terminal member of a size greatly reduced below that of the next to it. Even when there is thus a definite specialisation of the last member of the series it not infrequently happens that the addition, by variation, of a member beyond the normal terminal, is accompanied by a very palpable increase in size of the member which stands numerically in the place of the normal terminal.[2] So also with variation in the number of ribs, when a lumbar vertebra varies homoeotically into the likeness of the last dorsal and bears a rib, the rib placed next in front of this, which in the normal trunk is the last, shows a definite increase in development.
The consequences of such homoeoses are sometimes very extensive, involving readjustments of differentiation affecting a long series of members, as may easily be seen by comparing the vertebral columns of several individual Sloths[3] (whether Bradypus or Choloepus) to take a specially striking example.
It may be urged that no feature as yet enables us to perceive wherein lies the primary distinction which determines such variation, whether it is due to a difference in the dividing forces or in the material to be divided. If for instance we were to imitate such a series of segments by pressing hanging drops of a viscous fluid out of a paint-tube by successive squeezes, the number of times the tube is contracted before it is empty will give the number of the segments, but their size may depend either on the force of the contractions or on the capacity of the tube, or on various other factors. Nevertheless in the case of the variation of terminal members, whatever be the nature of the rhythmical impulse which produces the series of organs, the elevation of the normally terminal member in correspondence with the addition of another is what we should expect.
If the organism acquired its full size first and the delimitation of the parts took place afterwards, there might be some hope that the resemblance between living patterns and those mechanically caused by wave-motion might be shown to be a consequence of some real similarity of causation, but in view of the part played by growth, appeal to these mechanical phenomena cannot be declared to have more than illustrative value. Similarly in as much as living patterns appear, and almost certainly do in reality come into existence by a rhythmical process, comparisons of these patterns with those developed in crystalline structures, and in the various fields of force are, as it seems to me, inadmissible, or at least inappropriate.
However their intermittence be determined, the rhythms of division must be looked upon as the immediate source of those geometrically ordered repetitions universally characteristic of organic life. In the same category we may thus group the segmentation of the Vertebrates and of the Arthropods, the concentric growth of the Lamellibranch shells or of Fishes' scales, the ripples on the horns of a goat, or the skeletons of the Foraminifera or of the Heliozoa. In the case of plant-structures Church[4] has admirably shown, with an abundance of detail, how on analysis the definiteness of phyllotaxis is an expression of such rhythm in the division of the apical tissues, and how the spirals and "orthostichies" displayed in the grown plant are its ultimate consequences. The problem thus narrows itself down to the question of the mode whereby these rhythms are determined.
It is natural that we should incline to refer them to a chemical source. If we think of the illustration just given, of the segmentation of a viscous fluid into drops by successive contractions of a soft-walled tube we can, I think, conceive of such rhythmic contractions as due to summations of chemical stimuli, somewhat as are the beats of the heart. But when we recognize the vast diversity of materials the distribution of which is determined by an ostensibly similar rhythmic process it seems hopeless to look forward to a directly chemical solution. That the chemical degradation of protoplasm or of materials which it contains is the source of the energy used in the divisions cannot be in dispute, but that these divisions can be themselves the manifestations of chemical action seems in the highest degree improbable.
We may therefore insist with some confidence on the distinction between the Meristic and the substantive constitution of organisms, between, that is to say, the system according to which the materials are divided and the essential composition of the materials, conscious of the fact that the energy of division is supplied from the materials, and that in the ontogeny the manner in which the divisions are effected must depend secondarily on the nature of the substances to be divided. The mechanical processes of division remain a distinguishable group of phenomena, and variations in the substances to be distributed in division may be independent of variations in the system by which the distribution is effected.
Modern genetic analysis supplies many remarkable examples of this distinction. When formerly we compared the leaves of a normal palmatifid Chinese Primula with the pinnatifid leaves[5] of its fern-leaved variety we were quite unable to say whether the difference between the two types of leaf was due to a difference in the material cut up in the process of division or to a difference in that process itself. Knowledge that the distinction is determined by a single segregable factor tends to prove that the critical difference is one of substance. So also in the Silky fowl we know that the condition of its feathers is due to the absence of some one factor present in the normal form. We may conceive such differences as due to change of form in the successive "waves" of division, but we cannot yet imagine segregation otherwise than as acting by the removal or retention of a material element. Future observation by some novel method may suggest some other possibility, but such cases bring before us very clearly the difficulties by which the problem is beset.
Fig. 10. The palm-and fern type of leaf in Primula Sinensis.
The palm is dominant and the fern is recessive.