Accordingly, Moseley made the following measurements, beginning from the second and third whorls respectively:
| Width of | Ratio µ | |
|---|---|---|
| Six whorls | Three whorls | |
| 5·37 | 2·03 | 2·645 |
| 4·55 | 1·72 | 2·645 |
| Four whorls | Two whorls | Ratio µ |
| 4·15 | 1·74 | 2·385 |
| 3·52 | 1·47 | 2·394 |
“By the ratios of the two first admeasurements, the formula gives
r = (1·645)1 ⁄ 3 = 1·1804.
By the mean of the ratios deduced from the second two admeasurements, it gives
r = (1·389)1 ⁄ 2 = 1·1806.
“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 1·18.”
By similar and equally concordant observations, Moseley found for Turbo phasianus the characteristic ratio, 1·75; and for Buccinum subulatum that of 1·13.
From the table referring to Turbo duplicatus, on page [519], it is perhaps worth while to illustrate the logarithmic statement of the same facts: that is to say, the elementary corollary to the fact that the successive radii are in geometric progression, that their logarithms differ from one another by a constant amount. {521}
| Relative widths of successive whorls | Logarithms of successive whorls | Difference of successive logarithms |
|---|---|---|
| 131 | 2·11727 | — |
| 112 | 2·04922 | ·06805 |
| 94 | 1·97313 | ·07609 |
| 80 | 1·90309 | ·07004 |
| 67 | 1·82607 | ·07702 |
| 57 | 1·75587 | ·07020 |
| 48 | 1·68124 | ·07463 |
| 41 | 1·161278 | ·06846 |
| Mean difference ·07207 | ||