characters, of a given spiral shell may be determined, the only one of which much use has been made is that which Moseley first employed, namely, the simple method of determining {539} the relative breadths of the whorl at distances separated by some convenient vectorial angle (such as 90ô¯, 180ô¯, or 360ô¯).
Very elaborate measurements of a number of Ammonites have been made by Naumann23, by Sandberger24, and by Grabau25, among which we may choose a couple of cases for consideration. In the following table I have taken a portion of Grabauãs determinations of the breadth of the whorls in Ammonites (Arcestes)
| Breadth of whorls (180ô¯ apart) mm. | Ratio of breadth of successive whorls (360ô¯ apart) | The angle (öÝ) as calculated |
|---|---|---|
| 0ôñ30 | ã | ããô ãô |
| 0ôñ30 | 1ôñ333 | 87ô¯ô 23ÿ£¢ãý |
| 0ôñ40 | 1ôñ500 | 86ãô 19ã |
| 0ôñ45 | 1ôñ500 | 86ãô 19ã |
| 0ôñ60 | 1ôñ444 | 86ãô 39ã |
| 0ôñ65 | 1ôñ417 | 86ãô 49ã |
| 0ôñ85 | 1ôñ692 | 85ãô 13ã |
| 1ôñ10 | 1ôñ588 | 85ãô 47ã |
| 1ôñ35 | 1ôñ545 | 86ãô ã2ã |
| 1ôñ70 | 1ôñ630 | 85ãô 33ã |
| 2ôñ20 | 1ôñ441 | 86ãô 40ã |
| 2ôñ45 | 1ôñ432 | 86ãô 43ã |
| 3ôñ15 | 1ôñ735 | 85ãô ã0ã |
| 4ôñ25 | 1ôñ683 | 85ãô 16ã |
| 5ôñ30 | 1ôñ482 | 86ãô 25ã |
| 6ôñ30 | 1ôñ519 | 86ãô 12ã |
| 8ôñ05 | 1ôñ635 | 85ãô 32ã |
| 10ôñ30 | 1ôñ416 | 86ãô 50ã |
| 11ôñ40 | 1ôñ252 | 87ãô 57ã |
| 12ôñ90 | ã | ããô ãô |
| Mean | 86ô¯ô 15ÿ£¢ãý |
intuslabiatus; these measurements Grabau gives for every 45ô¯ of arc, but I have only set forth one quarter of these measurements, that is to say, the breadths of successive whorls measured