Fig. 312. Cyclammina cancellata, Brady.
subtended, though of less magnitude, are still remarkably constant, as we {597} may see by Fig. [313]; where the angle subtended by each chamber is made equal to 20°, and this diagrammatic figure is not perceptibly different from the other. In some cases the subtended angle is less constant; and in these it would be necessary to equate the several linear dimensions with the corresponding vector angles, according to our equation r = eθ cot α . It is probable that, by so taking account of variations of θ, such variations of r as (according to Rhumbler’s measurements) Pulvinulina and other genera appear to shew, would be found to diminish or even to disappear.
Fig. 313. Cyclammina sp. (Diagrammatic.)
The law of increase by which each chamber bears a constant ratio of magnitude to the next may be looked upon as a simple consequence of the structural uniformity or homogeneity of the organism; we have merely to suppose (as this uniformity would naturally lead us to do) that the rate of increase is at each instant proportional to the whole existing mass. For if V0 , V1 etc., be the volumes of the successive chambers, let V1 bear a constant proportion to V0 , so that V1 = q V0 , and let V2 bear the same proportion to the whole pre-existing volume: then
V2 = q(V0 + V1) = q(V0 + q V0)
= q V0(1 + q) and V2 ⁄ V1 = 1 + q.
{598}
This ratio of 1 ⁄ (1 + q) is easily shewn to be the constant ratio running through the whole series, from chamber to chamber; and if this ratio of volumes be constant, so also are the ratios of corresponding surfaces, and of corresponding linear dimensions, provided always that the successive increments, or successive chambers, are similar in form.