Br. F. A. Bather — Eocysiis. 53 



stroma, such as may sometimes be seen in contracting homogeneous 

 layers, preceded any extensive calcification, and that consequently 

 the stereom was concentrated at the nodes. On this assumption, 

 there arises a series of weight-points at the angles of alternating 

 hexagonal spaces. Inserting these on our plan (Diagr. p. 52), we 

 now proceed to fill in the other lines of stress that would flow 

 from such an arrangement. These have been represented in tlie 

 diagram with thicknesses roughly proportional to the distances 

 between the weight-points. Tlius a tri})le line connects the nodes 

 along the sides of the hexagon; a stout double line connects the 

 nodes horizontally ; a faint double line connects those at the upper 

 and lower angles, this being emphasized because the pull is intensified 

 in this direction by gravity ; a stout single line joins the node to the 

 nearer pair of the remaining angles, and a faint single line joins it to 

 the pair more remote. 



Now take this diagram, worked out on purely a priori reasoning 

 this night (December 5-6, 1917), and compare it with the lines of 

 Eigs. 2-6, drawn in 1900 before the problem had been formulated. 

 Starting from a node there are lines of stress precisely comparable 

 with the folds radiating from the umbo ; and it will be observed 

 that in the diagram no lines occur between the horizontal lines and 

 the immediateljr adjacent main lines, just as the plates are folded 

 very faintly or more often not at all in those spaces. 



So much for the folds ; now for the outline. If a circle be 

 described with the node as a centre, and with radius equal to half 

 the side of a hexagon, it will represent the tract that would 

 naturally be calcified if calcification spread uniformly outward from 

 the node until it met that spreading from the three adjacent nodes. 

 Known facts of growth, however, suggest that the calcification 

 would progress more rapidly along the main folds. Let the points 

 where these are cut by the circle be joined by straight lines, and an 

 irregular pentagon will result. This is shown in the diagram by 

 dotted lines, but these, instead of being quite straight, are bent 

 outwards slightly along the minor lines of stress. Thus is produced 

 an outline agreeing so closely with the outline of Fig. 7 that the 

 correspondence of theorj^ with fact is truly astonishing. 



The plates thus outlined in the diagram do not fill the whole 

 space; more particularly is there a large free area round the centre 

 of each hexagon. Probabh' the minor centres of calcification gave 

 rise to a number of small intercalary plates. 



If there be any truth in the hypothesis here put forward it follows 

 that the JEocystis plan represents an evolutionary stage previous to 

 that of the more usual pavement of hexagonal plates. One way in 

 which the change might have been effected would be the fusion and 

 growth of the plates about the centre of our supposed hexagon ; 

 this would produce a series of sub-hexagonal plates each surrounded 

 by smaller ones, much as in Beutocystis. Or the original pentagonal 

 plates, as they met, might be forced into a hexagonal shape, coupled 

 with a strengthening of the fold within the fork of the /^ ; this would 

 produce a plate like that of Amygdalocystis, which is not on the 

 normal plan. 



