genus whose little shells have built up vast tracts of carboniferous limestone over great part of European Russia8.
In this genus a growing surface of protoplasm may be conceived as wrapping round and round a small initial chamber, in such a way as to produce a fusiform or ellipsoidal shellãa transverse section of which reveals the close-wound spiral coil. The following are examples of measurements of the successive whorls in a couple of species of this genus.
| F. cylindrica , Fischer | F. BûÑcki , v. MûÑller | |||
|---|---|---|---|---|
| Breadth (in millimetres). | ||||
| Whorl | Observed | Calculated | Observed | Calculated |
| I | ôñ132 | ã | ôñ079 | ã |
| II | ôñ195 | ôñ198 | ôñ120 | ôñ119 |
| III | ôñ300 | ôñ297 | ôñ180 | ôñ179 |
| IV | ôñ449 | ôñ445 | ôñ264 | ôñ267 |
| V | ã | ã | ôñ396 | ôñ401 |
In both cases the successive whorls are very nearly in the ratio of 1ã₤:ã₤1ôñ5; and on this ratio the calculated values are based.
Here is another of von MûÑllerãs series of measurements of F. cylindrica, the measurements being those of opposite whorlsãthat is to say of whorls 180ô¯ apart:
| Breadth in mm. | ôñ096 | ôñ117 | ôñ144 | ôñ176 | ôñ216 | ôñ264 | ôñ323 | ôñ395 |
|---|---|---|---|---|---|---|---|---|
| Log. of mm. | ôñ982 | ôñ068 | ôñ158 | ôñ246 | ôñ334 | ôñ422 | ôñ509 | ôñ597 |
| Diff. of logs. | ã | ôñ086 | ôñ090 | ôñ088 | ôñ088 | ôñ088 | ôñ087 | ôñ088 |
The mean logarithmic difference is here ôñ088, =ã₤logã₤1ôñ225; or the mean difference of alternate logs (corôÙreôÙsponôÙding to a vector angle of 2ü, i.e. to consecutive measurements along the same radius) is ôñ176, =ã₤logã₤1ôñ5, the same value as before. And this ratio of 1ôñ5 between the breadths of successive whorls corresponds (as we see by our table on p. 534) to a constant angle of about {594} 86ô¯, or just such a spiral as we commonly meet with in the Ammonites9 (cf. p. 539).