| Ratio R ⁄ 1 | θ = 5° | 10° | 15° | 20° | 30° | 40° | 50° | 60° | 70° | 80° | 90° |
|---|---|---|---|---|---|---|---|---|---|---|---|
| 1·1 | 80° 8′ | 85° 0′ | 86° 44′ | 87° 28′ | 88° 16′ | 88° 39′ | 88° 52′ | 89° 0′ | 89° 4′ | 89° 7′ | 89° 8′ |
| 1·25 | 67 51 | 78 27 | 82 11 | 84 5 | 85 56 | 86 50 | 87 21 | 87 39 | 87 50 | 87 56 | 87 58 |
| 1·5 | 53 30 | 69 37 | 76 0 | 79 21 | 82 39 | 84 16 | 85 13 | 85 44 | 86 4 | 86 15 | 86 18 |
| 2·0 | 38 20 | 57 35 | 66 55 | 73 11 | 77 34 | 80 16 | 81 52 | 82 45 | 83 18 | 83 37 | 83 42 |
| 2·5 | 30 53 | 50 0 | 60 35 | 67 0 | 73 45 | 77 13 | 79 19 | 80 26 | 81 11 | 81 35 | 81 42 |
| 3·0 | 26 32 | 44 50 | 56 0 | 63 0 | 70 45 | 74 45 | 77 17 | 78 35 | 79 28 | 79 56 | 80 5 |
| 3·5 | 23 37 | 41 5 | 52 25 | 59 50 | 68 15 | 72 45 | 75 35 | 77 2 | 78 1 | 78 33 | 78 43 |
| 4·0 | 21 35 | 38 10 | 49 35 | 57 15 | 66 10 | 71 3 | 74 9 | 75 42 | 76 47 | 77 22 | 77 34 |
| 4·5 | 20 0 | 36 0 | 47 15 | 55 5 | 64 25 | 69 35 | 72 54 | 74 33 | 75 43 | 76 20 | 76 35 |
| 5·0 | 18 45 | 34 10 | 45 20 | 53 15 | 62 55 | 68 15 | 71 48 | 73 31 | 74 45 | 75 25 | 75 38 |
| 10·0 | 13 25 | 25 20 | 35 15 | 43 5 | 53 45 | 60 20 | 64 57 | 67 4 | 68 42 | 69 35 | 69 53 |
| 20·0 | 10 25 | 20 0 | 28 30 | 35 45 | 46 25 | 53 25 | 58 52 | 61 10 | 63 6 | 64 10 | 64 31 |
| 50·0 | 8 0 | 15 35 | 22 35 | 28 50 | 38 45 | 45 55 | 52 1 | 54 18 | 56 28 | 57 42 | 58 6 |
| 100·0 | 6 50 | 13 20 | 19 30 | 25 5 | 34 20 | 41 15 | 47 35 | 49 45 | 52 3 | 53 20 | 53 46 |
{559}
From this table, by interpolation, we may easily fill in the approximate values of α, as soon as we have determined the apical angle θ and measured the ratio R; as follows:
| R | θ | α | |
|---|---|---|---|
| Turritella sp. | 1·12 | 7° | 81° |
| Cerithium nodulosum | 1·24 | 15 | 82 |
| Conus virgo | 1·25 | 70 | 88 |
| Mitra episcopalis | 1·43 | 16 | 78 |
| Scalaria pretiosa | 1·56 | 26 | 81 |
| Phasianella bulloides | 1·80 | 26 | 80 |
| Solarium perspectivum | 1·50 | 53 | 85 |
| Natica aperta | 2·00 | 70 | 83 |
| Planorbis corneus | 2·00 | 90 | 84 |
| Euomphalus pentangulatus | 2·00 | 90 | 84 |
We see from this that shells so different in appearance as Cerithium, Solarium, Natica and Planorbis differ very little indeed in the magnitude of the spiral angle α, that is to say in the relative velocities of radial and tangential growth. It is upon the angle θ
Fig. 285. Terebra maculata, L.
that the difference in their form mainly depends: that is to say the amount of longitudinal shearing, or displacement parallel to the axis of the shell.
The enveloping angle, or rather semi-angle (θ), of the cone may be taken as 90° in the discoid shells, such as Nautilus and Planorbis. It is still a large angle, of 70° or 75°, in Conus or in Cymba, somewhat less in Cassis, Harpa, Dolium or Natica; it is about 50° to 55° in the various species of Solarium, about 35° in the typical Trochi, such as T. niloticus or T. zizyphinus, and about 25° or 26° in Scalaria pretiosa and Phasianella bulloides; it becomes a very acute angle, of 15°, 10°, or even less, in Eulima, Turritella or Cerithium. The costly Conus gloria-maris, one of the {560} great treasures of the conchologist, differs from its congeners in no important particular save in the somewhat “produced” spire, that is to say in the comparatively low value of the angle θ.
A variation with advancing age of θ is common, but (as Blake points out) it is often not to be distinguished or disentangled from an alteration of α. Whether alone, or combined with a change in α, we find it in all those many Gastropods whose whorls cannot all be touched by the same enveloping cone, and whose spire is accordingly described as concave or convex. The former condition, as we have it in Cerithium, and in the cusp-like spire of Cassis,