REPORT ON THE DEEP-SEA MEDUSAE. XVll 



§ 23. Primary cardinal number of the Medusa. In all Acraspedae, and in the majority 

 of Craspedotse, the original cardinal number of the Cnidariae (4) is invariably retained 

 (apart from numerous individual exceptions). The geometrical fundamental form of the 

 ordinary quadripartite Medusa is the quadrate pyramid or " quadrangular regular pyra- 

 mid " ; its base forms a square. Only two primary transverse axes exist (the two 

 diagonals of the square), and these cross at right angles. 



§ 24. Individual digressions from the primary or typical cardinal number. It is not 

 unusual to find individual abnormalities of the fundamental number (more frequently in 

 many groups or many species, more rarely in others), so that instead of four radii there 

 are six or eight, less commonly other numbers (5, 7, 9, &c.) ; in single species (e.g., 

 Aurelia aurita) this inclination to individual variation of the fundamental number is very 

 great ; in some groups (e.g., Cannotidae, System, taf. ix.) it is constant in many species 

 or genera, so that here of closely allied species or genera, some are quadripartite and 

 others sexpartite. In some other groups (iEquoridae, Cunanthidae, Peganthidae, Solmaridae) 

 the fundamental number is very large and indefinite ; it may mount up to above a 

 hundred (e.g., JEquorea forskalea. jE. ciliata, Mesonema ccsrulescens, M. dubium, &c). 

 The fundamental number is more inconstant the higher it rises, and therefore more 

 unequal in the different individuals of a species. 



§ 25. Secondary fundamental numbers of Medusae. Next to the primary fundamental 

 number 4, in the Medusae only 6, 8, and 12 are prominently significant as secondary 

 fundamental n ambers. They become hereditary in many species and groups of species, 

 and thereby acquire a systematic significance. On the other hand, the uneven numbers, 

 5 and 7, do not appear constantly in any single species of Medusa, but only as individual 

 variations, and so do 9, 10, and 11. As soon as we get beyond the number 12 the 

 fundamental number especially loses all morphological and systematic significance, as it 

 then becomes inconstant and variable, and more so the higher it rises (iEquoridae, 

 Cunanthidae, Peganthidae, Solmaridae). Moreover, as the fundamental number 8, which 

 often recurs, and is constant in many groups, has arisen by duplication of 4, as the more 

 unusual number 12 from duplication of 6, the most important secondary fundamental 

 number next to the primary 4 really consists of 6 ; instead of the normal 2 transverse 

 axes of the regular pyramid 3 are formed abnormally, and the hexagonal regular pyramid, 

 therefore, appears instead of the quadrangular. 



§ 26. Central and peripheric numbers. In all Medusae it is only the central part of 

 the body, pre-eminently the stomach, never the peripheric parts, which are the criterion 

 for determining the true fundamental number or homotypical number. The peripheric 

 parts, especially the umbrella margin with its appendages, show higher numbers than 

 the central part in the majority of Medusae. In most cases these higher numbers of the 

 peripheric parts have arisen either by multiplication from the lower fundamental number 

 of the central part or by regular multiplication according to definite conditions of pro- 



(ZOOL. CHALL. EXP. PART XII. — 1881.) M C 



