GRA.MMOCERAS. 159 



The progressive development of the genus Grartvmoceras may be divided into 

 four stages. 



1st. The Goniatite-stage (PI. XXVIII, figs. 11 — 13) seen in the interior whorls 

 of all species. 



2nd. The remains of an Arietan-stage (the sulcate stage) seen in young 

 Gramm. quadratum, Gramm. 8xma7bni, Gramm. toarcense, &c., but more frequently 

 omitted.^ 



3rd. Grammoceratan-stage. Examples : Gramm. striatulum, Gramm. doernense, 

 Gramm. Orbignyi, Gramm. fallaciosum, &c. 



4th. The Lioceratan-stage. Examples : Gramm. subserrodens, Gramm. leurum. 



The distinctive features of the genus Grammoceras are the shape of its ribbing 

 — subarcuate^ with a long ventral projection meeting the carina at an acute angle — 

 and the simple lobe-line with mere rudiments of auxiliary lobes. 



In his definition of this genus Hyatt said, " Abdomen keeled, but not 

 channeled." It is, however, impossible to limit the genus in this manner. The 

 ventral channels, which are well marked in Gramm. ovatum and Gramm. quad- 

 ratum, and are rudimentary in Gramm. toarcense and Gramm. Saernmmi^ are 

 merely the marks of descent from an Arietan ancestor. These species possess the 

 other features of the genus Grammoceras ; and as we follow the development of 

 the genus upwards we find that all traces of the Arietan-stage are omitted, and 

 that the compressed carinate whorl with narrow ventral area succeeds directly 

 upon the Goniatite-form.^ 



^ The omission of a stage of development may be formulated as a general rule. The accession 

 of a stage dissimilar to its predecessor, but approximately similar to any previously existing stage, 

 causes the gradual extinction of the intermediate stage or stages by the law of earlier inheritance 

 (Eule III, p. 134). The changes observable in the ventral area will fully explain this. Its develop- 

 ment is from (1) rounded to (2) bevelled, then (3) carinate, then (4) sulcate and carinate ; to the latter 

 succeeds a (5) carinate stage with the sulci becoming obsolete and merging into (G) the bevelled 

 stage. The omission of 4 and the merging of 3 and 5 into one longer stage, is exactly what would be 

 expected because it obviates a useless change. But 3 and 5 are in turn omitted for the same reason, 

 and if the form still continues to exist, a 7th stage — rounded — is added, and in the process of time tlie 

 omission of the intermediate stages causes 1 to pass directly into 7, and a rounded ventral area 

 again becomes the permanent feature. Grammoceras does not reach this state. The specimen of 

 Gramm. mactra (PI. XXXI, figs. 3, 4) shows the greatest reversion in the shape of its ventral area, 

 and the changes here are expressed as rounded, bevelled, to almost rounded. 



2 Subsigmoidal in the involute species only. 



^ It is much easier to obtain the inner whorls of these species than those of Lioceras, Hyper- 

 lioceras, &c., which often will not break up properly, and at other times are nothing but a mass of 

 crystal in which all structure of the inner whorl is obscured. When I wrote my remarks on the 

 evolution of the Hildoceratldse (pages 12S et seq.} I was quite unacquainted with what Prof. Hyatt had 

 written upon the evolution of other families. Although regretting that I had not before become 

 acquainted with such valuable and thoughtful work, yet I cannot but feel pleased that the conclusiouv^! 

 I arrived at concerning the mode of evolution among such Ammonites should agree so closely with 



