274 FAMILY NUMMULINIDA. 



higher rank than that of varieties. Taking the admirable monograph of MM. D'Archiac and 

 Haime as a guide, and testing the value of their specific differentiations by the knowledge 

 I have gained from the study of other types, and especially from that of OpercuUna, I find 

 that these are nearly all based upon characters which I have found to be so inconstant as to be 

 altogether fallacious. It is quite true that it would be a matter of no difficulty to pick out a 

 series of well-marked types presenting respectively the radiate, the sinuate, and the reticulate 

 arrangement of the septal prolongations, and characterised by great differences in figure and 

 proportion ; and under these types a large number of individuals might be unhesitatingly 

 arranged. But each series of individuals thus grouped together under one designation will 

 be sure to exhibit very considerable diversities ; and with every increase in the number com- 

 pared, especially when fresh specimens are brought from different localities,the range of these 

 diversities will be found to increase, and doubts will hence arise as to the place of particular 

 individuals, which mark the fallacy of any attempt to establish definite boundary lines between 

 the groups in question. Referring to my detailed comparison of different varieties of Opercu- 

 Una (xv) as affording the chief basis of my conclusions on this point, I might here limit 

 myself to the general statement that neither external form and proportions, the relative size of 

 the primordial chamber, the number and breadth of the convolutions, the number of chambers 

 in a convolution, the size and proportion of the chambers, the closeness with which the lateral 

 surfaces of the earlier convolutions are embraced by those which succeed them, the degree to 

 which the alar prolongations of the chambers extend themselves over the lateral surfaces, 

 nor the amount of non-tubular shell-substance which forms columns and plates within, and 

 shows itself on the surface in the granular tubercles or ridges with which it is occasionally 

 marked, — form any sufficient justification, either separately or collectively, for specific differen- 

 tiation. Nor, for the reasons already stated (^ 462), can I attach any higher value to 

 the course taken by the septal prolongations ; since, although they serve to mark three 

 primary types under which the numerous varieties may be distributed, they do not furnish 

 characters of sufficient definiteness and constancy for that absolute differentiation which is 

 required to satisfy the ordinary notion of a zoological species. — On this point I am happy to 

 find myself in full accordance with Messrs. Parker and Rupert Jones, by whom the relations 

 of the different forms of Nummulites have been studied far more systematically than they 

 have been by myself (lxxviii, lxxx h) ; their general conclusion being that " although it is 

 expedient to have binomial terms at hand wherewith to name the more important varieties of 

 NummuUnce, recent and fossil, yet for the purposes of philosophical zoology, NummuUua may 

 be recognised as a genus with but a single species, which, for our part, we should consider to 

 be typified by N. perforata." And it is obvious from Mr. Carter's recent investigations 

 (xxiii a) that he, too, has been led to feel the impossibility of clearly defining the species of 

 Nummulites; 



466. Affinities. — It cannot be requisite again to point out in detail the very intimate 

 nature of the affinity which exists between Nummulina and Operculina ; indeed the difficulty 

 lies in drawing a definite line of demarcation between them. For whilst in undoubted 

 OpercuIiiicB we occasionally find in tlie earlier whorls that the alar prolongations of the 

 chambers extend themselves over the lateral surfaces of the included spire even to its centre, 

 we often find in undoubted Nummulina, especially those of the radiate group, that the alar 



