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 Vÿ£¢0ã₤, Vÿ£¢1 etc., be the volumes of the successive chambers, let Vÿ£¢1 bear a constant proportion to Vÿ£¢0ã₤, so that Vÿ£¢1
=ã₤qãVÿ£¢0ã₤, and let Vÿ£¢2 bear the same proportion to the whole pre-existing volume: then
This ratio of 1ã₤ãã₤(1ã₤+ã₤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 corôÙreôÙsponôÙding surfaces, and of corôÙreôÙsponôÙding linear dimensions, provided always that the successive increments, or successive chambers, are similar in form.
We have still to discuss the similarity of form and the symmetry of position which characterise the successive chambers, and which, together with the law of continued proportionality of size, are the distinctive characters and the indispensable conditions of a series of ãgnomons.ã