358 



THE REV. H. MOSELEY ON THE GEOMETRICAL FORMS 



From these admeasurements we have, by the formula r = ((jt, — 1)"*, 



r = (1-45)* = 1-1318. 



Turbo phasianus. 



Three lines were drawn from the apex of this shell in different directions across its 

 whorls, and the following admeasurements were made upon them : 



The remarkable accordance of the measured with the calculated widths of the 

 whorls in this shell is to be attributed to the precision with which the line of sepa- 

 ration of the whorls is traced upon it. A great number of admeasurements were simi- 

 larly made upon other shells of the genera Trochus, Strombus and Murex ; some of 

 them were cut through the axis longitudinally; and similar measurements were made 

 by drawing lines from the apex across the section. From all these the same result 

 was obtained. ' 



Thus to each particular species of shell is annexed a characteristic number, being 

 the ratio of the geometric progression of similar successive linear dimensions of its 

 whorls ; from which number is deducible the constant angle of the particular loga- 

 rithmic spiral which is affected by that species of shell (see equation 26. in the fol- 

 lowing mathematical discussion). This number, or this angle, connected as it is 

 of necessity with the circumstances of the animal's growth and the manner of its 

 existence, is determinable by actual admeasurement, and may be available for the 

 purposes of classification ; it may suggest relations to which the observations of 

 naturalists may usefully be directed, and eventually become linked with character- 

 istic forms and modes of molluscous existence*. 



* The whole race of land shells, for instance, will certainly (from the nature of the case) be distinguished 

 from the aquatic shells by a wide difference in the numbers characteristic of the species of the two groups. 



