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 mm. | Percentage of pygidium | Segments in thorax | Segments in 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 Mesonacidæ, Solenopleuridæ, and Olenidæ, 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 palæontologists 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.