THE 

 LONDON, EDINBURGH, and DUBLIN 



PHILOSOPHICAL MAGAZINE 



AND 



JOURNAL OF SCIENCE. 



[FIFTH SERIES.] 



OCTOBER 1878. 



XXXII. On the Measurement of the Curves formed by Cephalo- 

 poda and other Mollushs. By the Rev. J. F. Blake, M.A., 



F.G.S* 



[Plate IV.] 



1. TT^ORTY years ago Professor Moseley pointed out (Phil. 



J- Trans. 1838) that the curves affected by discoid and 

 turbinated shells were derivable from the logarithmic spiral ; 

 and after him Naumann gave the name of concho-spiral to an 

 allied curve, in which the differences of the radii in the same 

 direction form a geometrical progression, but the initial radius 

 is not one of the series. By such a modification he hoped to 

 bring the measurements of actual shells more into harmony 

 with calculation. The errors of observation, however, are 

 always greater than this change would correct — if founded on 

 fact, which is doubtful ; and all practical advantage is lost by 

 the complication of the equations. 



In working through the fossil Cephalopoda, I have been 

 obliged to obtain some clearness of idea as to their mode of 

 origin and consequent connexion with each other, and to find 

 some means of recognizing in fragments the nature of the 

 whole ; and I have thus been led to the following results. 



2. If we examine the shell of a Nautilus in which the earlier 

 are preserved by the later whorls, we find that the shell bends 

 back upon itself as in fig. 1. Let A R B be the section of the 

 earliest stage, which in the Nautilus is nearly a semicircle. 

 On the growth of the shell, A B (the line in which the embryonic- 

 * Communicated by the Author. 



Phil. Mag. S. 5. Vol. 6. No. 37. Oct. 1878. R 



