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Detailed morphologic and anatomic investigation indicates a compound nature of the fossil growth-form known as Archimedes. Archimedes screws usually develop upon the outer edges of Fenestella zoaria and are made of the extended coiled mesh-work of this Bryozoa encrusted in the axis of the coiling by a protean organism, apparently an epizoic alga related to living kelps. The two symbionts formed intimate bryozoan-algal consortium, seemingly beneficial for both.

All species of Fenestella discovered as Archimedes symbionts were also found to form independent, noncoiled zoaria. Nine of such Fenestella species are newly described.

In America Archimedes ranges from Lower Devonian (Falls of Ohio River) to Lower Pennsylvanian (Utah), while in Russia it is found only in Upper Carboniferous and Lower Permian.

In the Lower Devonian only the loosely coiled Archimedes (called Helicopora by Claypole) is known, while in the other, younger rocks both loosely coiled and tightly coiled zoaria, with heavy central screw, are well represented.

Coiling of Archimedes is believed due to growth in whirlpools originating at proximal edge of some Fenestella colonies capable of producing food-bringing current. Only species of Fenestella with fine meshwork, having 2 to 3½ zooecia in fenestrule, produced tightly coiled Archimedes; species with coarser meshwork, 3 to 4 zooecia in fenestrule, produced lax Archimedes helicoids; and species with still coarser mesh-work, over 4 zooecia in fenestrules, did not coil.

The number of valid species, 13 of which are new, is: 1(?) in Upper Silurian; 1 in Lower Devonian; 8 in Keokuk and Warsaw and 23 in Chester of Mississippian; 5 in American Lower Pennsylvanian; and 8 in Russian and Arctic Upper Carboniferous and Permian.

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