breadths of adjacent, or immediately succeeding, whorls.
Here we have r =ã₤eÿ£¢2üã₤cotã₤öÝã₤, or logã₤r =ã₤logã₤eã₤ûã₤2üã₤ûã₤cotã₤öÝã₤, from which we obtain the following figures19:
| Ratio of breadth of each whorl to the next preceding r ã₤ãã₤1 | Constant angle öÝ |
|---|---|
| 1ôñ1ã | 89ô¯ô ã8ÿ£¢ãý |
| 1ôñ25 | 87ãô 58ã |
| 1ôñ5ã | 86ãô 18ã |
| 2ôñ0ã | 83ãô 42ã |
| 2ôñ5ã | 81ãô 42ã |
| 3ôñ0ã | 80ãô ã5ã |
| 3ôñ5ã | 78ãô 43ã |
| 4ôñ0ã | 77ãô 34ã |
| 4ôñ5ã | 76ãô 32ã |
| 5ôñ0ã | 75ãô 38ã |
| 10ôñ0ã | 69ãô 53ã |
| 20ôñ0ã | 64ãô 31ã |
| 50ôñ0ã | 58ãô ã5ã |
| 100ôñ0ã | 53ãô 46ã |
| 1,000ôñ0ã | 42ãô 17ã |
| 10,000ããã | 34ãô 19ã |
| 100,000ããã | 28ãô 37ã |
| 1,000,000ããã | 24ãô 28ã |
| 10,000,000ããã | 21ãô 18ã |
| 100,000,000ããã | 18ãô 50ã |
| 1,000,000,000ããã | 16ãô 52ã |
We learn several interesting things from this short table. We see, in the first place, that where each whorl is about three times the breadth of its neighbour and