XI] OF CERTAIN OPERCULA 773 



Accordingly, Moseley made the following measurements, begin- 

 ning from the second and third whorls respectively: 



Width of Ratio fi 



"By the ratios of the two first admeasurements, the formula 

 gives 



/•= (1-645)*= M804. 



By the mean of the ratios deduced from the second two admeasure- 

 ments, it gives 



r = (l-389)i = M806. 



"It is scarcely possible to imagine a more accurate verification 

 than is deduced from these larger admeasurements, and we may 

 with safety annex to the species Turbo duplicatus the characteristic 

 number M8." 



By similar and equally concordant observations, Moseley found 

 for Turbo phasianus the characteristic ratio, 1-75; and for Bucci- 

 num subulatum that of 1*13. 



From the measurements of Turritella dupUcata (on p. 772), it is 

 perhaps worth while to illustrate the logarithmic statement of the 

 same thing: that is to say, the elementary fact, or corollary, that if 

 the successive radii be in geometric progression, their logarithms will 

 differ from one another by a constant amount. 



Turritella duplicata 



And 0-07207 is the logarithm of 1-1805. 



