In _Cambarus_, the number of the branchiæ is reduced to seventeen by the disappearance of the last pleurobranchia; while, in _Astacoides_, the process of reduction is carried so far, that only twelve complete branchiæ are left, the rest being either represented by mere rudiments, or disappearing altogether. _The branchial formula of Astacoides._ Somites and Arthrobranchiæ their Podobranchiæ. /───────^───────\ Pleuro- Appendages. Anterior. Posterior. branchiæ. VII. 0 (ep. r.) 0 0 0 = 0 (cp. r.) VIII. 1 _r_ 0 0 = 1 + _r_ IX. 1 1 0 0 = 2 X. 1 1 _r_ 0 = 2 + _r_ XI. 1 1 _r_ 0 = 2 + _r_ XII. 1 1 _r_ 0 = 2 + _r_ XIII. 1 1 _r_ 0 = 2 + _r_ XIV. 0 0 0 1 = 1 6 + _ep. r_ 5 + _r_ + 0 + 4 _r_ + 1 = 12 + _ep. r._ + 5 _r_. {267} As these formulæ show, those trichobranchiate crustacea, which possess fewer than twenty-one complete branchiæ on each side, commonly present traces of the missing ones, either in the shape of epipodites, as in the case of the podobranchiæ, or of minute rudiments, in the case of the arthrobranchiæ and the pleurobranchiæ. In the marine, prawn-like, genus Penæus (fig. 73, Chap. VI.), the gills are curiously modified trichobranchiæ. The number of functional branchiæ is, as in the lobster, twenty; but the study of their disposition shows that the total is made up in a very different way. _The branchial formula of Penæus._ Somites and Arthrobranchiæ. their /───────^───────\ Pleuro- Appendages. Podobranchiæ. Anterior. Posterior. branchiæ. VII. 0 (ep.) 1 0 0 = 1 + ep. VIII. 0 (ep.) 1 1 1 = 3 + ep. IX. 0 (ep.) 1 1 1 = 3 + ep. X. 0 (ep.) 1 1 1 = 3 + ep. XI. 0 (ep.) 1 1 1 = 3 + ep. XII. 0 (ep.) 1 1 1 = 3 + ep. XIII. 0 1 1 1 = 3 XIV. 0 0 0 1 = 1 ── ── ── ── ── 0 + 6 ep. + 7 + 6 + 7 = 20 + 6 ep.