XI] 



IN CERTAIN AMMONITES 



539 



the relative breadths of the whorl at distances separated by some 

 convenient vectorial angle (such as 90°, 180°, or 360°). 



Very elaborate measurements of a number of Ammonites have 

 been made by Naumann*, by Sandbergerf, and by GrabauJ, 

 among which we may choose a couple of cases for consideration. 

 In the following table I have taken a portion of Grabau's deter- 

 minations of the breadth of the whorls in Ammonites (Arcesles) 



A m monltes iiifuslabiatus. 

 Ratio of breadth of 



* Naumann, C. F., Ueber die Spiralen von Conchylien, Abh. k. sacks. Ges. pp. 153- 

 196, 1846 ; Ueber die cyelocentrische Conchospirale u. iiber das Windungsgesetz von 

 Planorhis corneus, ibid, i, pp. 171-195, 1849; Spirale von Nautilus u. Ammonites 

 galeatus, Ber. k. sacks. Ges. n, p. 26, 1848; Spirale von Amm. Ramsaueri, ibid, xvi, 

 p. 21, 1864: see also Poggendorjfs Annalen, l, p. 223, 1840; u, p. 245, 1841 ; uv, 

 p. 541, 1845, etc. 



f Sandberger, G., Spiralen des Ammonites Amaltkeus, A. Gaytani, und Goniatites 

 ititumescens, Zeitsckr. d. d, Geol. Gesellsck. x, pp. 446-449, 1858. 



J Grabau, A. H.. Ueber die Naumannscke Conckospirale, etc. Inauguraldiss. 

 Leipzig, 1872: Die Spiralen von Conckylien, etc. Programm, Nr. 502, Leijjzig, 

 1882. 



