498 BULLETIN 100, UNITED STATES NATIONAL MUSEUM 



We have designated the distal portion of the zoarium the terminal 

 border, its form depends rigorously on the inferior angle of the initial 

 V and is mathematically inverse to it. The wider the inferior angle 

 the smaller the distal angle (Flabellopora acuta) ; the more the inferior 

 angle approaches 90 degrees the larger is the distal angle (Flabellopora 

 transversa). When the inferior angle is close to 180 degrees the colony 

 becomes orbicular (Flabellopora lenticularis) . The initial angle is 

 not constant in the same species although the amount of the varia- 

 tions is so small that all the colonies of the same species have almost 

 the same form. 



The zooecia of the initial base are smaller, but their walls are 

 very thick. The growth is peripheral but it is essential that the 

 first zooecium formed be on the branch of the initial V and it is for 

 this reason that one frequently finds incomplete zooecia on the edge 

 of the terminal border and almost always at its distal extremity. 



Biology. — The colonies of Flabellopora float freely; they are not 

 attached at all and are not supported on any substratum. They 

 are all experienced aquatic equilibrists. We are certain that all the 

 bryozoa are masters of hydraulics and that certain forms like Rete- 

 pora and Frondipora are marvellous architects but Flabelloporas , 

 with the same qualities are preeminent geometricians. Their 

 symmetry is perfect and their internal structure is the expression of a 

 rigorous calculation without any visible error. Each colony is an 

 absolute geometrical construction, an algebraic equation solved. 

 This mathematical exactness does not exclude elegance of form 

 (F. elegans), richness of ornamentation (F. tuberosa), variety of 

 aspect (F. variabilis), multiplicity of details (F. tubifera), or strange- 

 ness of appearance (F. asper). 



Such an architecture is possible only in calm, tranquil waters in 

 sheltered and little frequented localities, where nothing can derange 

 the small workers. 



There are no sand grains, no calcareous particles in our sections 

 in the vicinity of the ancestrula. The larva chooses then as a sup- 

 port a minute organic fragment. It envelops it in its develop- 

 ment and destroys it after its transformation. Then begins in the 

 mysterious obscurity of the oceanic depths the magnificent work of 

 construction which will make of each colony a marvel of architecture, 

 a masterpiece of hydraulics. 



The Flabelloporas live free above the submarine bottom. They 

 are not immobile for their general form is fashioned for vertical 

 movements. As the ascending motion is more laborious and more 

 difficult than the descending movement the terminal angle of the 

 colony is smaller than the inferior angle of the initial base. But 

 this colony does not elevate itself very high; it does not proceed at 

 hazard like a fish. In effect the Flabelloporas are rare; they are not 



