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sides of the opposite lamellæ. In Zygospira the loop is simple, but arched or forming a double bow-like curve (Figs. 7376). In Dayia there is a simple process from the centre of the saddle running toward the base of the crura (see Fig. 81, c). There is added a bifurcated end in Whitfieldia (81, f). In Athyris (81, h) the ends of the branches are curved over to partly cover the primary lamellæ of the spirals. In Kayseria they are continued along parallel to the lamellæ of the spiral coil (81, 2). This extension is only seen in the late Mesozoic forms. In Meristella (j) the branches of the process recurve and join together, forming on each side a loop, resembling the handles of a pair of scissors.

In this series of modifications the extreme degree of elaboration is met with among the Meristellinæ, and this subfamily was well represented among the Eosilurian faunas.

Characters of the Brachidium found to be good Distinctive Characters of Genera.-It has been acknowledged by all the more advanced students of Brachiopods, that the modifications of the brachidium are the most important characters to be found for determining the generic and higher affinities of these interesting forms, and great and most painstaking labor has been expended within the past ten or fifteen years in working out the structure of their delicate parts.

We may interpret this experience of systematists to mean that the various degrees of modification observed in these parts are found to be constant among species which by likeness in other characters are associated together into groups to form genera.

Plasticity a Characteristic of their Early Initial Stage.-We have already seen by analysis of the characters that almost without exception the plasticity of the characters, and the expression of the widest range of possible differentiation in each particular direction, were characteristics of the early stage in the history of the Helicopegmata. By the beginning of the Neosilurian the expansion of differentiation had reached its extreme in almost every particular.

Evolution of the Characters of the Brachidium Relatively Rapid. ---When we consider that we have knowledge of only a few small types of this whole order earlier than the Eosilurian, and

that the Helicopegmata lived on to the middle of the Mesozoic, and, third, that most species have a life-period of a third or half of the duration of the whole Silurian time, it is no exaggeration to say that the evolution of these modifications of the brachidium was, relatively to all laws of organic change in geology, extremely rapid.

Rate of Initiation of the Genera of Helicopegmata.-If now we reduce the facts of generic differentiation to graphic form, we find that the sudden or rapid differentiation is a fact, and is not due to imperfect evidence. Considering, as in previous cases, classification to be a mode of expressing degrees of difference, we may rely upon the mathematical relations of initiation of the groups of equal rank as an expression of the rate of initiation of new characters in general, or an approximate measure of the rate of geological evolution.

TABLE EXPRESSING THE RATE OF EXPANSION OF THE FAMILY, SUBFAMILY, AND GENERIC CHARACTERS OF THE HELICOPEGMATA.

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The Helicopegmata as a suborder is found to be represented in three family types of structure: one of these appeared first in the Ordovician, in a single subfamily, a single or possibly two genera, and but few species. At the opening of the next era, the Upper Silurian, the other two families appear, and seven out of the known twelve subfamilies were initiated.

If we consider the actual total number of generic types for the whole suborder, and some of the later of these genera are based upon very slight modification of characters, we find 76 in all. The rate of their initiation is: Ord. 2, Sil. 20, Dev. 16, Carb. 10, Trias. 16, Jur. 2; or by the time of the second stage in which any of the suborders are known one quarter of the total generic differentiation had taken place, and differentiation did not cease till six eras had been passed and the suborders became extinct.

Representing these facts in whatever way we may, they are positive in testifying to a rapid and early expression of the differences in structure which have served as the means of distinguishing different families, subfamilies, and genera; and a close inspection of the figures seems to indicate that in proportion to the higher taxonomic rank of the characters, the earlier or more rapid was their initiation.

General Law of Rate of Initiation of Generic Characters.-In general terms, the scientific fact here noted, irrespective of any theoretical explanation, is that, relative to the known. geological range of species of the Helicopegmata, the grander differences in structure were very early to appear, and that the progress of differentiation after this early stage was largely in respect of varietal and specific characters and proportionally small in characters of higher rank.

The Life-period of Genera and the Initiation of a New Genus. -We have now examined some of the laws of genera as exhibited in the case of the Helicopegmata. The characters which are found to be of generic value, such as the particular structure of the calcareous framework supporting the brachial arms, have a definite history. Examining all the known Brachiopods, from the beginning of geologic time to the present, it is found that the structural characters peculiar to this suborder are confined to the time extending from the Lower Silurian to the Triassic or Jurassic era. As a particular example, for instance, the arrangement of the brachidium characteristic of the genus Meristella (see Fig. 81, j, with the complex loop forming two lateral rings, and the cone of the spirals pointing to the lateral margin of the shell, as in Fig. 80, a) begins in the Silurian, and is never seen after the Devo

nian. The genus is said to be characteristic of that period; and not only in America, but in Europe, in China, in South America, wherever Paleozoic rocks are known, Meristella is found characteristically in the Upper Silurian, running rarely a little below, but more frequently above, into the Devonian.

There comes a time in the history of organisms of a particular line of descent, when a certain definite arrangement of the parts of the organism becomes conspicuous, as this particular loop of the Meristella; the occurrence of individuals developing this peculiarity is limited below and above. This arrangement differs from that of the corresponding part in any other animals of the same time; and all the animals exhibiting this character may be considered as closely allied genetically, because in other characters they also show strong resemblance. This state of things is evidence of the beginning or initiation of a new genus.

If all the specimens known possessing this new character were examined and classified, they would be found to have minor differences of form, surface marking, etc., which furnish criteria for dividing them into several distinct species. Geologically, one of these species is the first to appear; it lives but a short time relatively, or it may continue to live during several periods. It is peculiar to one country, or it is the same throughout the world wherever the genus appears; but whether there be many or few species, the character which is called a generic character begins at some particular time: during a certain period it is frequently met with; after a time it ceases, and is never known to appear again. The particular combination of characters on some one organism constitutes its generic characters, and we may say that the genus so characterized has a certain definite life-period.

During the Life-period of the Genus its Characters Constant.While other characters may vary, these generic characters do not change sufficiently to be noticed as of importance to the paleontologist. Not only the generic, but the family and the ordinal, characters, which are associated together under the generic name Meristella, are thus constant for all the specimens examined.

A Culminating Point or Acme in the Life-period of a Genus.— Again, we observe that the fossil specimens which present the characters (of Meristella for instance) are most abundant along the middle of this period; for the Meristellas it is about the Neosilurian; also in that period they are more frequently met with in distant parts of the world; and where they are most abundant the characters which serve to distinguish them into separate species are more numerous; and both before that epoch and afterward there are fewer and fewer, until we reach both ends, where the species are very rare.

Summary of the Geological Characteristics of a Genus.-To generalize the above observations, it may be said that the genus practically has a time of beginning and a time of ending. Practically, that is, according to the knowledge we possess, there was a geological time, represented by a particular horizon in the geological series of strata, when each genus began; there was a particular period, of shorter or longer extent, during which the genus was freely propagated, and abundant individuals flourished, leaving their remains in the strata, wherever the conditions were appropriate for their preservation. The genus had a period of decadence, or of growing old, the species became fewer and fewer, the individuals more rare, and finally the genus died out, and, so far as our knowledge goes, became extinct. These laws apply to Meristella, and in substance they apply to all genera we know of. The period from the initiation to the extinction of the genus is the life-period of that genus.

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