a time: making use of the following property of a geometrical progression, that ãif ôç represent the ratio of the sum of every even number ( m ) of its terms to the sum of half that number of terms, then the common ratio ( r ) of the series is represented by the formula
Accordingly, Moseley made the following measurements, beginning from the second and third whorls respectively:
| Width of | Ratio ôç | |
|---|---|---|
| Six whorls | Three whorls | |
| 5ôñ37 | 2ôñ03 | 2ôñ645 |
| 4ôñ55 | 1ôñ72 | 2ôñ645 |
| Four whorls | Two whorls | Ratio ôç |
| 4ôñ15 | 1ôñ74 | 2ôñ385 |
| 3ôñ52 | 1ôñ47 | 2ôñ394 |
ãBy the ratios of the two first admeasurements, the formula gives
By the mean of the ratios deduced from the second two admeasurements, it gives
ãIt 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 charôÙacôÙterôÙisôÙtic number 1ôñ18.ã
By similar and equally concordant observations, Moseley found for Turbo phasianus the charôÙacôÙterôÙisôÙtic ratio, 1ôñ75; and for Buccinum subulatum that of 1ôñ13.
From the table referring