The eight genera of the Mesonacidae, _Nevadia_, _Mesonacis_, _Elliptocephala_, _Callavia_, _Holmia_, _Wanneria_, _Paedeumias_, and _Olenelloides_, have an average of 20.25 segments in the thorax and 1.5 in the pygidium, a total of 21.75. If, however, the curious little _Olenelloides_ be omitted, the average for the thorax rises to 22.14 and the total to 23.84. _Olenelloides_ is, in fact, very probably the young of an _Olenellus_. Specimens are only 4.5 to 11 mm. long, and occur in the same strata with _Olenellus_ (see Beecher 1897 A, p.

191).

Thirty-three genera from the Middle Cambrian afford data as to the number of segments, the Agnostidae being excluded. The extreme of variation there is smaller than in the Lower Cambrian. The number of thoracic segments varies from 2 in Pagetia to 25 in _Acrocephalites_, and these same genera show the greatest range in total number of trunk segments, 8 and 29 respectively.

The average of thoracic segments for the entire thirty-three genera is 10.5, of pygidial segments 5.9, a total average of 16.4. It will be noted that the thorax shows on the average less and the pygidium more segments than in the Lower Cambrian. If the Agnostidae could be included, this result would doubtless be still more striking. Of the genera considered, _Asaphiscus_ with 7-11 thoracic and 5-8 pygidial segments, _Blainia_ with 9 thoracic and 6-11 pygidial, _Zacanthoides_ with 9 thoracic and 5 pygidial, and _Anomocare_ with 11 thoracic and 7-8 pygidial segments came nearest to the average. Only a few departed widely from it. The genera tabulated were _Acrocephalites_, _Alokistocare_, _Crepicephalus_, _Karlia_, _Hamburgia_, _Corynexochus_, _Bathyuriscus_, Poliella, _Agraulos_, _Dolichometopus_, _Ogygopsis_, _Orria_, _Asaphiscus_, _Neolenus_, _Burlingia_, _Blainia_, _Blountia_, _Marjumia_, _Pagetia_, _Eodiscus_, _Goniodiscus_, _Albertella_, _Oryctocara_, _Zacanthoides_, _Anomocare_, _Anomocarella_, _Coosia_, _Conocoryphe_, _Ctenocephalus_, _Paradoxides_, _Ptychoparia_, _Sao_, and _Ellipsocephalus_.

Enough genera of Upper Cambrian trilobites are not known from entire specimens to furnish satisfactory data. Excluding from the list the Proparia recently described by Walcott, the average total trunk segments in ten genera is 18, but as most of the genera are Olenidae or olenid-like, not much weight can be attached to these figures.

For the Cambrian as a whole, the average for sixty-two genera is between 17 and 18 trunk segments, which is surprisingly like the result obtained by Carpenter from only twelve genera, and tends to indicate that it must be somewhere near the real average. If the 5 or 6 segments of the head be added, it appears that the "average" number of segments is very close to the malacostracan number 21. Genera with 16 to 18 trunk segments are Callavia, _Protypus_, _Bathynotus_, _Crepicephalus_, _Bathyuriscus_, _Ogygopsis_, _Burlingia_, _Orria_, _Asaphiscus_, _Blainia_, _Zacanthoides_, _Neolenus_, _Anomocare_, _Conocoryphe_, _Saukia_, _Olenus_, and _Eurycare_.

The order Proparia originated in the Cambrian, and Walcott has described four genera, one from the Middle, and three from the Upper.

The number of segments in these genera is of interest. _Burlingia_, the oldest, has 14 segments in the thorax and 1 in the pygidium. Of the three genera in the Upper Cambrian, _Norwoodia_ has 8-9 segments in the thorax and 3-4 in the pygidium; _Millardia_ 23 in thorax and 3-4 in pygidium; and _Menomonia_ 42 in thorax and 3-4 in pygidium. It is of considerable interest and importance to note that the very elongate ones are not from the Middle but from the Upper Cambrian.

Forty genera of Ordovician trilobites known from entire specimens were tabulated, and it was found that the range in the number of segments in the thorax and pygidium was surprisingly large. _Agnostus_, which was not included in the table, has the fewest, and _Eoharpes_, with 29, the most. While the range in number of segments in the thorax is 2 to 29, the range of the number in the pygidium, 2 to 26, is almost as great. A species of _Dionide_ has 26 in the pygidium, while _Remopleurides_ and _Glaphurus_ have evidence of only 2. The average number of segments in the thorax for the forty genera was 10.15, in the pygidium 8.81, and the average number for the trunk 19.

Genera with just 19 segments in the trunk appear to be rare in the Ordovician, a species of _Ampyx_ being the only one I have happened to notice. _Calymene_, _Tretaspis_, _Triarthrus_, _Asaphus_, _Ogygites_, and _Goldius_ come with the range of 18 to 20. _Goldius_, with 10 segments in the thorax and (apparently) 8 in the pygidium, comes nearest to the averages for these two parts of the trunk. _Goldius_, _Amphilichas_, _b.u.mastus_, _Acidaspis_, _Actinopeltis_, and _Sphaerexochus_ are among the genera having 10 segments in the thorax, and there are many genera which have only one or two segments more or less than 10.

In most Ordovician genera, thirty-five out of the forty tabulated, the number of segments in the thorax is fixed, and the variation is in any case small. In four of the five genera where it was not fixed, there was a variation of only one segment, and the greatest variation was in _Pliomerops_, where the number is from 15 to 19. This of course indicates that the number of segments in the thorax tends to become fixed in Ordovician time. The variation in the number of segments in the pygidium is, however, considerable. It is difficult in many cases to tell how many segments are actually present in this shield, as it is more or less smooth in a considerable number of genera. Extreme cases of variation within a genus are found in _Encrinurus_, species of which have from 7 to 22 segments in the pygidium, _Cybeloides_ with 10 to 20, and _Dionide_ with 10 to 26. As the number in the thorax became settled, the number in the pygidium became more unstable, so that not even in the Ordovician can the total number of segments in the trunk be said to show any tendency to become fixed.

The genera used in this tabulation were: _Eoharpes_, _Cryptolithus_, _Tretaspis_, _Trinucleus_, _Dionide_, _Raphiophorus_, _Ampyx_, _Endymionia_, _Anisonotus_, _Triarthrus_, _Remopleurides_, _Bathyurus_, _Bathyurellus_, _Ogygiocaris_, _Asaphus_, _Ogygites_, _Isotelus_, _Goldius_, _Cyclopyge_, _Amphilichas_, _Odontopleura_, _Acidaspis_, _Glaphurus_, _Encrinurus_, _Cybele_, _Cybeloides_, _Ectenonotus_, _Calymene_, _Ceraurus_, _Pliomera_, _Pliomerops_, _Pterygometopus_, _Chasmops_, _Eccoptochile_, _Actinopeltis_, _Sphaerexochus_, _Placoparia_, _Pilekia_, _Selenopeltis_, and _Calocalymene_.

Only sixteen genera of Devonian trilobites were available for tabulation, and it is not always possible to ascertain the exact number of segments in the pygidium, although genera with smooth caudal shields had nearly all disappeared. The number of segments in the thorax had become pretty well fixed by the beginning of the Devonian, _Cyphaspis_ with a range of from 10 to 17 furnishing the only notable exception. The range for the sixteen genera is from 8 to 17, the average 11, the number exhibited by the Phacopidae which form so large a part of the trilobites of the Devonian. The greater part of the species have large pygidia, and while the range is from 3 to 23, the average is 11.2. _Probolium_, with 11 in the thorax and 11-13 in the pygidium, and _Phacops_, with 11 in the thorax and 9-12 in the pygidium, approach very closely to the "average" trilobite, and various species of other genera of the Phacopidae have the same number of segments as the norm. In every genus, however, the number of segments in the pygidium is variable, the greatest variation being in _Dalmanites_, with a range of from 9 to 23. The number of segments in the pygidium was therefore not fixed and was on the average higher than in earlier periods.

The genera used in the tabulation were: _Calymene_, _Dipleura_, _Goldius_, _Proetus_, _Cyphaspis_, _Acidaspis_, _Phacops_, _Hausmania_, _Coronura_, _Odontochile_, _Pleuracanthus_, _Calmonia_, _Pennaia_, _Dalmanites_, _Probolium_, and _Cordania_.

The trilobites of the late Palaeozoic (Mississippian to Permian) belong, with two possible exceptions, to the Proetidae, and only three genera, _Proetus_, _Phillipsia_, and _Griffithides_, appear to be known from all the parts. I am, however, a.s.suming that both _Brachymetopus_ and _Anisopyge_ have 9 segments in the thorax, and so have tabulated five genera. The range in the number of segments in the pygidium is large, from 10 in some species of _Proetus_ to 30 in _Anisopyge_, and the average, 17.3, is high, as is the average for total number in the trunk, 26.3. _Anisopyge_, a late Permian trilobite described by Girty from Texas, is perhaps the last survivor of the group. It seems to have had 39 segments in the trunk, making it, next to the Cambrian _Paedeumias_ and _Menomonia_, the most numerously segmented of all the trilobites.

The above data may be summarized in the following table:

Period No. of Av. No. of Av. No. of Av. No.

genera segments in segments in of trunk thorax pygidium segments ========================================================== Lower Cambrian 19 13.9 3.7 17.6 Middle Cambrian 33 10.5 5.9 16.4 Entire Cambrian 62 ... ... 17-19 Ordovician 40 10.15 8.81 18.96 Devonian 16 11 11.2 22.2 Late Palaeozoic 5 9 17.3 26.3

This table confirms that made up by Carpenter, and shows even more strikingly the progressive increase in the average number of segments in the trunk throughout the Palaeozoic.

While the two trilobites with the greatest number of segments are Cambrian, yet on the average, the last of the trilobites had the more numerously segmented bodies. The multisegmented trilobites are:

Period Genus Av. No. of Av. No. of Av. No.

segments in segments in of trunk thorax pygidium segments ================================================================ Lower Cambrian _Paedeumias_ 44+ 1 45+ Upper Cambrian _Menomonia_ 42 4 46 _Ectenonotus_ 12 22 34 Ordovician _Encrinurus_ 11 22 33 _Dionide_ 6 26 32 Silurian _Harpes_ 29 3 32 Devonian _Coronura_ 11 23 34 _Dalmanites_ 11 23 34 Permian _Anisopyge_ 7+(9?) 30 39?

_Anisopyge_, the last of the trilobites, stands third on the list of those having great numbers of segments, and in each period there are a few which have considerably more than the average number. It may be of some significance that of these nine genera only _Paedeumias_ and _Anisopyge_ belong to the Opisthoparia, the great central group, and that five are members of the Proparia, the latest and most specialized order.

FORM OF THE SIMPLEST PROTASPIS.

It would naturally be expected that the young of the Cambrian trilobites should be more primitive than the young of species from later formations, and Beecher (1895 C) has shown that this is the case. He had reference, however, chiefly to the eyes, free cheeks, and spines, and by comparison of ontogeny and phylogeny, demonstrated the greater simplicity of the protaspis which lacked these organs. It remains to inquire which among the other characteristics are most fundamental.

Among the trilobites of the Lower Cambrian, no very young have been seen except of Mesonacidae. Of these, the ontogeny of _Elliptocephala asaphoides_ Emmons is best known, thanks to Ford, Walcott, and Beecher, but, as the last-named has pointed out, the actual protaspis or earliest shield has not yet been found. The youngest specimen is the one roughly figured by Beecher (1895 C, p. 175, fig. 6). It lacks the pygidium, but if completed by a line which is the counterpart of the outline of the cephalon, it would have been 0.766 mm. long. The pygidium would have been 0.183 mm. long, or 23 per cent of the whole length. The axial lobe was narrow, of uniform width along the cephalon, showed a neck-ring and four indistinct annulations, but did not reach quite to the anterior end, there being a margin in front of the glabella about 0.1 mm. wide. The greatest width of the cephalon was 0.66 mm., and of the glabella 0.233 mm., or practically 35 per cent of the total width. Other young _Elliptocephala_ up to a length of 1 mm., and young _Paedeumias_, _Mesonacis_, and _Holmia_ (see Kiaer, Videnskaps, Skrifter, 1 Mat.-Naturv. Kla.s.se, 1917, No. 10) show about the same characteristics, but all these have large compound eyes on the dorsal surface and specimens in still younger stages are expected.

It may be pointed out, however, that in these specimens the pygidium is proportionately larger than in the adult. Walcott cites one adult 126 mm. long in which the pygidium is 6 mm. long, or between 4 and 5 per cent of the total length, while in the incomplete specimen described above, it was apparently 23 per cent. In a specimen 1 mm.

long figured by Walcott, the pygidium is 0.15 mm. long, or 15 per cent of the whole length.

The development of several species of trilobites from the Middle Cambrian is known. Barrande (1852) described the protaspis of _Sao hirsuta_, _Peronopsis integer_, _Phalacroma bibullatum_, _P. nudum_, and _Condylopyge rex_. Broegger figured that of a _Liostracus_ (Geol.

For. Forhandl., 1875, pl. 25, figs. 1-3) and Lindstroem (1901, p. 21) has reproduced the same. Matthew (Trans. Roy. Soc. Canada, vol. 5, 1888, pl. 4, pls. 1, 2) has described the protaspis of a _Liostracus_, _Ptychoparia linnarssoni_ Broegger, and _Solenopleura robbi_ Hartt.

Beecher (1895 C, pl. 8) has figured the protaspis of _Ptychoparia kingi_ Meek, and the writer that of a Paradoxides (Bull. Mus. Comp.

Zool., vol. 58, No. 4, 1914, pl. i).

_Sao_, _Liostracus_, _Ptychoparia_, and _Solenopleura_ all have the same sort of protaspis. In all, the axial lobe reaches the anterior margin and is somewhat expanded at that end; in all, the glabella shows but slight trace of segmentation; and in all, the pygidium occupies from one fifth to one fourth the total length. There is considerable variation in the width of the axial lobe. It is narrowest in _Ptychoparia_, where in the middle it is only 14 per cent of the whole width, and widest in _Solenopleura_, where it is 28 per cent. In _Ptychoparia_ the pygidium of the protaspis occupies from 18 to 22 per cent of the whole length. In the adult it occupies 10 to 12 per cent.

In _Solenopleura_ it makes up about 26 per cent of the protaspis, and in the adult about 8 per cent.

In the youngest stages of all these trilobites, the pygidium is incompletely separated from the cephalon. The first sign of segmentation is a transverse crack which begins to separate the cephalon and pygidium, and by the time this has extended across the full width the neck segment has become rather well defined. In this stage the animal is prepared to swim by means of the pygidium, and first becomes active. The coincident development of the free pygidium and the neck-ring strongly suggests that the dorsal longitudinal muscles are attached beneath the neck-fur row.

The single protaspis of _Paradoxides_ now known, while only 1 mm.

long, is not in the youngest stage of development. It is like the protaspis of _Olenellus_ in having large eyes on the dorsal surface and a narrow brim in front of the glabella. The glabella is narrower than in the adult.

The initial test of no agnostid has probably as yet been seen, as all the young now known show the cephalon and pygidium distinctly separated. _Phalacroma bibullatum_ and _P. nudum_ are both practically smooth and isopygous when 1.5 mm. long. _P. bibullatum_ shows no axial lobe at this stage, but a wide glabella and median tubercle develop later, and when the glabella first appears, it extends to the anterior margin. In _Peronopsis integer_ and _Condylopyge rex_, the axial lobe is outlined on each of the equal shields in specimens about 1 mm.

long, but is without furrows and reaches neither anterior nor posterior margin.

From the foregoing brief description it appears that the pygidium of the protaspis varies in different groups from as little as 15 per cent of the total length in the Mesonacidae to as much as 50 per cent in the Agnostidae; that the axial lobe varies from as little as 14 per cent of the total width in one _Ptychoparia_ to as much as 50 per cent in _Phalacroma nudum_; that the glabella reaches the anterior margin in the Olenidae, Solenopleuridae, and _Phalacroma bibullatum_, while there is a brim in front of it in the Olenellidae, Paradoxidae, and three of the species of the Agnostidae. The decision as to which of these conditions are primitive may be settled quite satisfactorily by study of the ontogeny of the various species.

ORIGIN OF THE PYGIDIUM.

Taking first the pygidium, it has already been pointed out that in each case the pygidium of the adult is proportionally considerably smaller than the pygidium of the protaspis. The stages in the growth of the pygidium are better known in Sao hirsuta than in any other trilobite, and a review of Barrande's description will be advantageous.

Barrande recognized twenty stages in the development of this species, but there was evidently a still simpler protaspis in his hands than the smallest he figured, for he says, after describing the specimen in the first stage: "We possess one specimen on which the head extends from one border to the other of the disk, but as this individual is unique we have not thought it sufficient to establish a separate stage." This specimen is important as indicating a stage in which there was not even a suggestion of division between cephalon and pygidium.

In the first stage described by Barrande, the form is circular, the length is about 0.66 mm., and the glabella is narrow with parallel sides and no indications of lateral furrows. The neck segment is indicated by a slight prominence on the axial lobe, and back of it a constriction divides the axial lobe of the pygidium into two nodes, but does not cross the pleural lobes. The position of the nuchal segment permits a measurement of the part which is to form the pygidium, and shows that that shield made up 30 per cent of the entire length.

In the second stage, when the test is 0.75 mm. long, the cephalon and pygidium become distinctly separated, and the latter shield shows three annulations on the axial and two pairs of ribs on the pleural lobes. It now occupies 33-1/3 per cent of the total length.

In the third stage, when the total length is about 1 mm., the pygidium has continued to grow. It now shows five annulations on the axial lobe, and is 46 per cent of the total length.

In the fourth stage, two segments of the axial lobe have been set free from the front of the pygidium. The length is now 1.5 mm. and the pygidium makes up 32 per cent of the whole. From this time the pygidium continues to decrease in size in proportion to the total length, as shown in the following table.

Stage Length in Percentage Segments in Segments in mm. of pygidium thorax pygidium ======================================================== 1 0.66 30 0 2 2 0.75 33-1/3 0 3 3 1.00 46 0 5 4 1.50 32 2 5-6 5 1.50 25 3 4 6 1.75 23 4 4 7 1.80 21 5 3 8 2.00 17 6 3 9 2.50 13 7 3 10 3.00 12 8 3 11 3.50 11 9 3-4 12 4.00 11 10 3-4 13 5.00 10 11 3 14 5.50 9 12 2-4 15 6.00 8 13 3-4 16 6.50 8 14 3 17 7.00 7 15 3 18 7.50 7 16 3 19 7.50 6 17 2 20 10.25 6 17 2

This table shows the rapid increase in the length of the pygidium till the time when the thorax began to be freed, the very rapid decrease during the earlier part of its formation until six segments had been set free, and then a more gradual decrease until the entire seventeen segments had been acquired, after which time the relative length remained constant. From an initial proportion of 30 per cent, it rose to nearly one half the whole length, and then dwindled to a mere 6 per cent, showing conclusively that the thorax grew at the expense of the pygidium.

If this conclusion can be sustained by other trilobites, it indicates that the large pygidium is a more primitive characteristic of a protaspis than is a small one. I have already shown that the pygidium is proportionately larger in the protaspis in the Mesonacidae, Solenopleuridae, and Olenidae, and a glance at Barrande's figures of _"Hydrocephalus" carens_ and _"H." saturnoides_, both young of _Paradoxides_ will show that the same process of development goes on in that genus as in _Sao_. There is first an enlargement of the pygidium to a maximum, a rise from 20 per cent to 33 per cent in the case of _H. carens_ and then, with the introduction of thoracic segments, a very rapid falling off. All of these are, however, trilobites with small pygidia, and it has been a sort of axiom among palaeontologists that large pygidia were made up of a number of coalesced segments. While not definitely so stated, it has generally been taken to mean the joining together of segments once free. The asaphid, for instance, has been thought of as descended from some trilobite with rich segmentation, and a body-form like that of a _Mesonacis_ or _Paradoxides_.

The appeal to the ontogeny does not give as full an answer to this question as could be wished, for the complete life-history of no trilobite with a large pygidium is yet known. While the answer is not complete, enough can be gained from the study of the ontogeny of _Dalmanites_ and _Cyclopyge_ to show that in these genera also the thorax grows by the breaking down of the pygidium and that no segment is ever added from the thorax to the pygidium. The case of _Dalmanites socialis_ as described by Barrande (1852, p. 552, pl. 26) will be taken up first, as the more complete. The youngest specimen of this species yet found is 0.75 mm. long, the pygidium is distinctly separated from the cephalon, and makes up 25 per cent of the length.

This is probably not the form of the sh.e.l.l as it leaves the egg. At this stage there are two segments in the pygidium, but they increase to four when the test is 1 mm. long. The cephalon has also increased in length, however, so that the proportional length is the same. The subjoined table, which is that compiled by Barrande with the proportional length of the pygidium added, is not as complete as could be desired, but affords a very interesting history of the growth of the caudal shield. The maximum proportional length is reached before the introduction of thoracic segments, and during the appearance of the first five segments the size of the pygidium drops from 25 to 15 per cent. Several stages are missing at the critical time between stages 8 and 9 when the pygidium had added three segments to itself and has supplied only one to the thorax. This would appear to have been a sort of resting or recuperative stage for the pygidium, for it increased its own length to 20 per cent, but from this stage up to stage 12 it continued to give up segments to the thorax and lose in length itself. After stage 12, when the specimens were 8 mm. long, no more thoracic segments were added, but new ones were introduced into the pygidium, until it reached a size equal to one fifth the entire length, as compared with one fourth in the protaspis.

Stage Length Percentage Segments in Segments in in mm. of pygidium thorax pygidium ==================================================== 1 0.75 25 0 2 2 0.75 25 0 3 3 1.00 25 0 4 4 1.00 22 1 3 5 1.25 20 2 3 6 1.25 18 3 3 7 1.60 15 4 3 8 1.60 15 5 3 9 3.00 20 6 6 10 3.50 20 7 6 11 8.00 18 9 7 12 8.00 16 11 5 13 12.00 16 11 7 14 19.00 18 11 9 15 95.00 20 11 11

Since the above was written, Troedsson (1918, p. 57) has described the development of _Dalmanites eucentrus_, a species found in the Brachiopod shales (Upper Ordovician) of southern Sweden. This species follows a course similar to that of _D. socialis_, so that the full series of stages need not be described. The pygidium is, however, of especial interest, for there is a stage in which it shows two more segments than in the adult. Troedsson figures a pygidium 1.28 mm. long which has eight pairs of pleural ribs, while the adult has only six pairs. The ends of all these ribs are free spines, and were the development not known one would say that this was a case of incipient fusion, while as a matter of fact, it is incipient freedom.