It is a feature common to these and to all other rhythmical repetitions produced by purely mechanical forces that there is resemblance between the members of the series, and that this similarity of conformation may be maintained in most complex detail. When however in the mechanical series some of the members differ from the rest we have no difficulty in recognising that these differences--which correspond with the differentiations of the organic series--are due to special heterogeneity in the conditions or in the materials, and it never occurs to us to suppose that all the members must have been primordially alike. For example, in the case of ripple-marks on the sand, which I choose as one of the most familiar and obvious illustrations of a repeated series due to mechanical agencies, if we notice one ripple different in form from those adjacent to it, we do not suppose that this variation must have been brought about by deformation of a ripple which was at first formed like the others, but we ascribe it to a difference in the sand at that point, or to a difference in the way in which the wind or the tide dealt with it. We may press the analogy further by observing that in as much as such a series of waves has a beginning and an end, it possesses polarity like that of the various linear series of parts in organisms, and even the formation of each member must influence the shape of its successor. Since in an organism the beginning and end of the series are always included, some differentiation among the repetitions must be inevitable. If therefore it be conceded, as I think it must, that segmentation and pattern are the consequence of a periodic process we realize that it is at least as easy to imagine the formation of such a series of parts having family likeness combined with differentiation as it would be to conceive of their arising primordially as a series of identical repetitions. The suggestion that the likenesses which we now perceive are the remains of a still more complete resemblance is a substitution of a more complex conception for a simpler one. The other question raised by the problem of Serial Homology is how far there is a correspondence between individual members of series when the series differ from each other either in the number of parts, or in the mode of distribution of differentiation among them. Students, for example, of vertebrate morphology debate whether the _n_th vertebra which carries the pelvic girdle in Lizard A is individually homologous with the _n_ + _x_th vertebra which fulfils this function in Lizard B, or whether it is not more truly homologous with the vertebra standing in the _n_th ordinal position, though that vertebra in Lizard B is free.