512 THE FORMS OF TISSUES [ch. 



twenty-five facets in a line from a central one, the total number in the entire 

 field is (3 X 25 X 26) + 1 = 1951 *. 



The electrical engineer is dealing with the selfsame problem when he finds 

 he can pack 6 + 18 + 36+ ... wires around a central wire, to form a multiple 

 cable of 1, 2 and 3 concentric strands. He coimts them by the same formula, 

 in the simpler form of 6<+ 1 : where t is a "triangular number," 1, 3, 6, 10, etc., 

 corresponding to the number of strands. Thus 1951=6x325 + 1; 325 being 

 the triangular number of 25, 1 + 2 + 3 + . . . + 25. 



We have many varied examples of this principle among corals, 

 wherever the polypes are in close juxtaposition, with neither empty 

 space nor accumulations of matrix between their adjacent walls. 

 Favosites gothlandica, for instance, furnishes us with an excellent 

 example. In the great genus Lithostrotion we have some species 

 which are "massive" and others which are "fasciculate." In other 

 words, in some the long cylindrical corallites are closely packed 

 together, and in others they are separate and loosely bundled (Fig. 

 190); in the former the corallites are squeezed into hexagonal 

 prisms, while in the latter they retain their cylindrical form. Where 

 the polypes are comparatively few, and so have room to spread, 

 the mutual pressure ceases to work or only tends to push them 

 asunder, letting them remain circular in outhne (e.g. Thecosmilia). 

 Where they vary gradually in size, as for instance in Cyathophyllum 

 hexagonum, they are more or less hexagonal but are not regular 

 hexagons; and where there is greater and more irregular variation 

 in size, the cells will be on the average hexagonal, but some will 

 have fewer and some more sides than six, as in the annexed figure 

 of Aracknophyllum (Fig. 192). Where larger and smaller cells, 

 corresponding to two different kinds of zooids, are mixed together, 

 we may get various results. If the larger cells are numerous enough 



* This estimate neglects not merely the broken hexagons, but all those whose 

 centres lie between the circle and a hexagon inscribed in it. The discrepancy 

 is considerable, but a correction is easily made. It will be found that the numbers 

 arrived at by the two methods are approximately as 6:5. For more detaOed 

 calculations see a paper by H.M. (? H. Munro) in Q.J. M.S. vi, p. 83, 1858. The 

 methods of enumeration used by older writers, especially by Leeuwenhoek, are 

 sometimes curious and interesting; cf. Hooke, Micrographia, 1665, p. 176; 

 Leeuwenhoek, Arcana naturae, 1695, p. 477; Phil. Trans. 1698, p. 169; Epist. 

 physiolog. 1719, p. 342; Swammerdam, Biblia Naturae, 1737, p. 490. Leeuwenhoek 

 found, or estimated, 3181 facets on the cornea of a scarab, and 8000 on that of 

 a fly; M. Puget, about the same time, found 17,325 in that of a butterfly. See also 

 Karl Leinemann, Die Zahl der Facetten in den. . .Coleopteren, Hildesheim, 1904. 



