Thanks to the discovery of very early larval stages of the American Olenellus asaphoides, which FORD[9] and WALCOTT[10] have described and figured, we can through combination of these decipher the development and signification of the facial ridges. To facilitate my explanation I here join a series of cuts from the earliest stage to the more developed, with addition of two schematic stages to complete in a certain degree the series of WALCOTT and FORD.[11] See figures p. 13. [Footnote 9: In American Journ. of Science 1877 p. 265 and 1881 p. 250.] [Footnote 10: Bullet. U. S. Geol. Survey N:o 30, 1886, pl. 17 fig. 5-6.--Tenth Annual Rept. U. S. Geol. Survey, 1888-89, printed 1890, plate 88, fig. 1, 1 a.] [Footnote 11: In his paper on »The larval stages of Trilobites» p. 175 BEECHER gives a new figure (f. 6), original from FORD'S collection, of the larva of Ol. asaphoides, but it is so sketchy that I cannot with certainty make out what it means. I cannot agree with him when he speaks of free cheeks and eyes in these and he is completely wrong when he says that the outer pair of spines belong to the free cheeks etc. (p. 176).] The figure 1 has been hypothetically composed as a deduction from fig. 2, which presupposes an earlier stage of development like that in fig. 1, when there existed three or four pair of lateral appendages in the larva. This then consists of a central portion of five segments. The large anterior crescentlike segment does not, however, show any distinction between a central part and lateral appendages, it is nearly as large as the three next taken together and its backwards bent side horns embrace the next two posterior segments and attain with their narrow pointed tips the back of the fourth segment. The central portion consists of five segments, when the somewhat not well definite posterior marginal segment is taken in account. Each of these segments excepting the fifth one has lateral appendages, those of the second and third segment being quite as broad as the central part and bent backwards in a curve ending in a small pointed spine. The lateral appendages of the fourth segment are largest of all, more than double the length of the two next in front, triangular and standing out beyond the posterior border of the shell as a broad spine.