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Originally appearing in Volume V27, Page 283 of the 1911 Encyclopedia Britannica.
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TRILOBITES, extinct Arthropoda, formerly classified with the Crustacea, but of late years relegated to the Arachnida (q.v.), which occurred abundantly in seas of the Cambrian and Silurian periods, but disappeared entirely at the close of the Palaeozoic epoch. Both their origin and the causes which led to their extinction are quite unknown. Widely diver-gent forms make their appearance suddenly in the Cambrian period amongst the earliest known fossils; and the high perfection. of structure to which they had at that time attained Powers of Reciprocals rithms in the formulae (25) and (26) of Natural Numbers. (31) sec x=(-I)° (2n+I)r (2n+I . z"x)2-x2, and expand each term of this series in powers of x2, then we get sec x=Z„ V'+24 3xz 26 .x4 where x must lie between =Ir. By comparing the series (31), (32), (33) with the expansions of cot x, tan x, sec x obtained otherwise, we can calculate the values of U2, U4... V2, V4... and WI, W3.... When U„ has been found, V,, may be obtained from the formula 2e V" = (2"—I) Un. For Lord Brounker's series of r, see CIRCLE. It can be got at once Continued by putting a = 1, b = 3, c = 5 .... in Euler's Factors I I I I a2 b2. for r. theorem =a—b+c—... =a+b—a+c—b+... Sylvester gave (Phil. Meg., 1869) the continued fraction sr I I.2z_33_4 2—I+1+ 1+ 1+ I+...' which is equivalent to Wallis's formula for sr. This fraction was originally given by Euler (Comm. Acad. Petrojol. vol. xi.) ; it is also given by Stern (in Crelle's Journ. vol. x.). 3o. It may be shown by means of a transformation of the series sin x x x2 x2 x3 Continued for cos x and x that tan x=-- 3 — 5 — 7 — Fractions x= implies the antecedent existence of much simpler types, and refers I the origin of life to a date immeasurably distant from that at which we have actual proof of the existence of animal and vegetable organisms. However different in structure Trilobites may be, they all agree in possessing a head-shield usually semi-circular in shape, which results from the fusion of apparently five segments, and bears, except in some blind forms, a pair of large reniform compound eyes like those of the king-crab (Xiphosura). This head-shield is succeeded by a varying number of free segments, each of which consists of a medium convex tergal piece and a pair of arched lateral plates, the pleura, of which there is one on each side. The terga and pleura of each individual segment overlap those of the segment that serially succeeds it. The mid-region of the body, composed of jointed segments, is followed by a larger or smaller region consisting of fused segments and termed the pygidium or caudal shield, which in some cases is as large as the head-shield itself, in other cases much smaller. When the pygidium is large and composed of many segments, the number of free body segments is correspondingly reduced, and vice versa. It is with respect to this number of segments that respectively constitute the pygidium and the mid-region of the body that Trilobites differ most markedly from each other; and it is a singular fact that the extremes in structural organization in this particular to be met with in the Trilobita are found side by side in strata of Cambrian age. In Paradoxides, for example, there are about twenty freely movable segments followed by a very short and small pygidium, whereas in Agnostus the freely movable segments are reduced to two and the pygidium is as large as the cephalic shield. In this genus the number of segments composing the pygidium is obscured, as also it is in the genus Illaenus, which has as many as ten movable segments pre-ceding the large semi-circular pygidium; but in such forms as Ogygia and Asaphus, which have about eight free segments, the sutural lines on the pygidium indicate that it is composed of about a dozen or more segments. Somewhat resembling Agnostus is Microdiscus, with four movable segments and a large pygidium consisting of about five fused segments, the lines of union between the latter being clearly indicated. The tergal and pleural elements of the pygidium are generally well marked. They are also well marked on the cephalic shield, the tergal elements being represented by a median axial elevated area showing indistinct signs of segmentation, and a lateral unsegmented plate, the gena, which carries the eyes. The posterolateral angles of the gena are commonly produced into spiniform processes, which may project backwards beyond the middle of the body as in Paradoxides, or considerably beyond its posterior termination as in Trinucleus or Ampyx. The latter is further remarkable for having the median area of the head-shield, the flabellum, produced into an anteriorly directed spike. For many years only the dorsal surface of Trilobites was known, nothing having been ascertained of the ventral surface and appendages. Comparatively recently, however, specimens have been obtained with the ventral surface exposed, revealing the number and structure of the limbs. A pair of the latter was articulated to the sides of a moderately wide dorsal plate on each segment of the body, and similar limbs were attached to the ventral surface of the head-shield behind the mouth. Each of these limbs was two-branched, the external branch consisting of a slender fringed flagellum possibly respiratory in function, and the inner of a normal jointed ambulatory leg. These two branches arose from a common basal segment or coxa, the inner surface of which was produced into a strong process underlying the external area. In the region of the mouth the basal segments were armed with teeth and subserved the purpose of mastication. As in all Arachnida there is only a single pair of appendages in front of the mouth, and these were one-branched, long and filiform and acted as antennae. Under the pygidium or caudal shield the appendages were much shortened, and their main branch consisted of broader and flatter segments than those of the preceding limbs. Such was the structure of the appendages in Trilobites belonging to the genus Triarthrus; but considering the great structural differences that obtain between Triarthrus and many other genera, it would be rash to assume that there were not corresponding differences in the structure of the limbs. It must not indeed be assumed that those of the first pair were in all cases antenniform. It is probable that no .satisfactory classification of the Trilobites will be proposed until the limbs of most of the genera have been examined. Up to the present time all attempts to arrange the genera in natural and definable groups have failed to meet with general approval; and this criticism must be extended to Beecher's subdivision of the class into three orders, named Hypoparia, Proparia and Opisthoparia, based upon the form and position of a groove, the so-called genal suture, which marks the lateral portion of the head-shield. In the majority of Trilobites this groove passes backwards from the anterior or anterolateral edge of this plate to its posterior or postero-lateral border, dividing it into an inner portion continuous with the flabellum and fused tergal regions, and an outer portion bearing the eye. Those genera, like Paradoxides, Olenus, Asaphus, Phillipsia and others, in which this groove cuts the posterior edge of the head-shield on the inner side of its angle are referred to the Opisthoparia; those, like Dalmanites and Phacops, in which it cuts the lateral border in front of the posterior angle, belong to the Proparia. But in certain genera, like Conocoryphe, Calymmene and Triarthrus, it cuts the margin of the head-shield so close to the posterior angle that the distinction between the two groups practically breaks down. To the Hypoparia belongs a comparatively small number of genera, like Trinucleus and Aquastus, in which this groove or genal suture is beneath the margin of the head-shield and does not appear upon its upper surface. In external form Trilobites are not unlike Isopod Crustaceans, especially the terrestrial species commonly called " woodlice "; and until the nature of their appendages was known, it was thought by some authorities that the two groups might be related. Like the woodlice they were capable of rolling themselves up into a ball, many specimens having been found fossilized in this state, with the pygidium pressed tightly against the head-shield. There is very little doubt that they lived at the bottom of the sea, feeding upon worms or other soft marine organisms, crawling slowly about the sandy or muddy bottom and burying themselves beneath its surface when danger threatened. That these animals were widely distributed in former times is proved by their occurrence at the present day in palaeozoic fossiliferous strata both of the northern hemisphere and of Australia; and despite the fact that their remains have not been found in rocks of the Mesozoic or Kainozoic epochs, it was conceived to be possible that living specimens might be dredged from the sea-floor during the exploration of the ocean depths undertaken by the " Challenger " expedition. Needless to say this faint hope was not borne out by results. (R. I. P.)
End of Article: TRILOBITES
TRILEMMA (Gr. Tp(Zt, three, X~7µµa, something tak...

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