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 shell 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