XIV. 0 0 0 1 = 1 ── ── ── ── ── 6 + ep. r. + 6 + 5 + 4 = 21 + ep. r. {265} This tabular “branchial formula” exhibits at a glance not only the total number of branchiæ, but that of each kind of branchia; and that of all kinds connected with each somite; and it further indicates that the podobranchia of the first thoracic somite has become so far modified, that it is represented only by an epipodite, with branchial filaments scattered upon its surface. In _Palinurus_, these branchial filaments are absent and the branchial formula therefore becomes— Somites and Arthrobranchiæ. their Podobranchiæ. /───────^───────\ Pleuro- Appendages. Anterior. Posterior. branchiæ. VII. 0 (ep.) 0 0 0 = 0 (ep.) VIII. 1 1 0 0 = 2 IX. 1 1 1 0 = 3 X. 1 1 1 0 = 3 XI. 1 1 1 1 = 4 XII. 1 1 1 1 = 4 XIII. 1 1 1 1 = 4 XIV. 0 0 0 1 = 1 ── ── ── ── ── 6 + ep. + 6 + 5 + 4 = 21 + ep. In the lobster, the solitary arthrobranchia of the eighth somite disappears, and the branchiæ are reduced to twenty on each side. In _Astacus_, this branchia remains; but, in the English crayfish, the most anterior of the pleurobranchiæ has vanished, and mere rudiments of the two next remain. It has been mentioned that other _Astaci_ present a rudiment of the first pleurobranchia. {266} _The branchial formula of Astacus._ Somites and Arthrobranchiæ their Podobranchiæ. /───────^───────\ Pleuro- Appendages. Anterior. Posterior. branchiæ. VII. 0 (ep.) 0 0 0 = 0 (ep.) VIII. 1 1 0 0 = 2 IX. 1 1 1 0 = 3 X. 1 1 1 0 = 3 XI. 1 1 1 0 or _r_ = 3 or 3 + _r_ XII. 1 1 1 _r_ = 3 + _r_ XIII. 1 1 1 _r_ = 3 + _r_ XIV. 0 0 0 1 = 1 ── ── ── ── ── 6 + ep. + 6 + 5 + 1 + 2 or 3_r_ = 18 + ep. + 2 or 3_r_.