of the Transition Formations of the Rhine. 11 



lobes, four sections among the Goniatites with the simple 

 dorsal lobe, and two amongst those with the dorsal lobe di- 

 vided, that follow however a determinate law in their geo- 

 gnostic distribution. To these six proposed sections, among 

 the Goniatites properly so called, might perhaps be added as 

 a seventh the Ceratites of the muschelkalk : they are un- 

 doubtedly more nearly allied to the Goniatites than on some 

 Ammonites of the more recent formations. The Goniatites and 

 Ceratites united, would stand opposed to the Ammonites, and 

 might like them be divided into several natural families. 



Before I proceed to the individual description of the differ- 

 ent species, I consider it necessary to explain the determination 

 of the proportions of these fossils, characteristics introduced 

 for the first time into the science by M. von Buch, and of 

 which I have also availed myself in the description of the se- 

 veral species. The increase in diameter, the height of the 

 spire, or more simply the height, expresses the proportion in 

 which the height of the mouth increases in the space of an 

 entire whorl. The height of the mouth is measured on two 

 succeeding whorls, and the lesser of these dimensions is put 

 down as a decimal fraction of the greater, which is taken for 

 unity. The height of the mouth may be estimated in two 

 ways : by taking the perpendicular dropped from the middle 

 of the back, either as far as the suture or as far as the middle 

 of the back of the preceding whorl. As the degree of involu- 

 tion in the outer circles is always the same as in the inner 

 circles, we ought by these two estimations to obtain the same 

 result for the increase in height. The increase in breadth, or 

 simply the breadth, expresses the proportion in which the 

 breadth of the mouth (that is to say, the dimension perpen- 

 dicular to the height) increases in the space of an entire whorl 

 — measure again here the breadth on two whorls which cover 

 each other, and set down the lesser number as a decimal frac- 

 tion of the greater. The increase in height and the increase 

 in breadth are very certain proportions for the different spe- 

 cies ; taken together with the involution, these characters 

 completely determine the form of an Ammonite. The thick- 

 ness which expresses the proportion between the height and 

 the breadth of the mouth depends on the two first propor- 

 tions ; it varies in each respect whenever the height (and 



