MACROCEPHALITES. 39 



established in Schlotheim's ' Taschenbuch ' in 1813 by the reference "Ammonites 

 macrocephalus, ' Oryct., Norica, Suppl.,' tab. xii, fig. 8." (Sec text-fig. 3, p. fc3.) 

 On making this reference to Baier's work, which neither d'Orbigny nor Zittel 

 appear to have done, it is seen at once that the species represented is thai now 

 called A. tumidus after Reinecke (1818). Accordingly in Schlotheim's ' Petre- 

 factenkunde ' in 1820 we find "A. tumidus, Reinecke," quoted as a synonym. 

 He now includes numerous varieties under the name, which when a genus is 

 established become species of that genus. Thus Macrocephalites macrocephalus, 

 Schloth., sp., is the name of the shell called by Reinecke Ammonites tumidus, and 

 the figure given by d'Orbigny as Ammonites macrocephalus and by Zittel as 

 Macrocephalites macrocephalus is without an appropriate name. 



From a stratigraphical point of view, pure and simple, there is no doubt some 

 advantage in speaking of " the zone of Am. macrocephalus," for it represents ;m 

 epoch in the world's history when a certain type of ammonite occupied an 

 extremely wide area; but in this sense "the zone of Macrocephalites," using a 

 generic term only, would serve the purpose equally well, if we would follow the 

 history of Ammonites or trace their appearance in the strata. 



Of the characters of Macrocephalites some depend upon age. It does not 

 appear, however, that any marked change occurs in youth, or at all events that am- 

 is observable; but as the whorls grow the number of ribs does not keep an 

 absolute constancy, or even a proportion to the breadth of the whorl, but some- 

 thing between these two, increasing in number two or three in half a whorl. The 

 sutures also become more complex, the inner whorls showing the merest outline of 

 those of the adult ; but in large specimens the outer whorls become quite smooth 

 or nearly so (terebratus). These changes must be allowed for in any case. Other 

 characters, such as the direction of the ribs, especially those which unite, the place 

 and character of their union, the form of the umbilical edge, etc., can only be 

 appreciated by the eye ; but there are others which are capable of numerical 

 expression, and therefore of accurate statement, so long as they remain constant. 

 These are : 1 



(1) The ratio of the transverse to the greatest diameter (l>). 



(2) The ratio of the last whorl to the greatest diameter (/). 



(3) The ratio of the thickness to the diameter. 



(-1) The number of the ribs which cross the periphery in half a whorl. 

 (5) The ratio of this number to that of those passing to the umbilicus. 

 The size of the umbilicus, and the amount of overlapping of the whorls, art' 

 not required, being dependent on the above and defined by the equations — 

 Umbilicus^ 1 _ h (1 + 1 2) am] , . = b-t s 

 Diameter 1 ' l bt * 



on the assumption that the characters remain constant. 



1 See my paper "On the Measurement of the Curves formed by Cephalopoda and other 

 Mollusca," ' Phil. Mag.,' 1878. 



