Page:Proceedings of the Royal Society of London Vol 4.djvu/103

Rh sidered is, that the grov/th of the animal, corresponding to a given increment in the angle of the generating curve, v/ili always be pro- portional to the bulk it has then attained : and if the physical vital energies of the animal be proportional to its actual bulk, its growth, in any given time, v/ill be proportional to its grovv'th up to that time. Hence the whole angle of revolution of the curve generating the shell mil be proportional to the whole corresponding time of the animal's growth ; and therefore, the whole number of whorls and parts of whorls will, at any period, be proportional to its age.

The form of the molluscous animal remaining always similar to itself, the surface of the organ by which it deposits its shell will vary as the square of the linear dimensions ; but as the deposition of its shell must vary as the cube of the same dimensions, there must be an increased functional activity of the organ, varying as the sim- ple linear dimensions.

Since to each species of shell there must correspond a particular number expressing the ratio of the geometrical progression of the similar successive linear dimensions of the Vv^horls ; and since the constant angle of the particular logarithmic spiral, which is affected by that species of shell, is deducible from this number, the author considers that, connected as the form of the shell is with the cir- cumstances of the animal's growth and the manner of its existence, this number, or the angle of the particular spiral, determinable as it is in each case by actual measurement, may be available for the purposes of classification, and may suggest relations by which, eventually, they may become linked with characteristic forms, and modes of molluscous existence.

The concluding portion of the paper contains a mathematical dis- cussion of certam geometrical and mechanical elements of a con- choidal surface. These are, the extent of the surface itself ; the vo- lume contained by it ; the centre of gravity of the surface, and also of the volume, in each case, when the generating figure revolves about a fixed axis without any other motion, and also when it has, besides this, a motion of translation in the direction of that axis ; and, lastly, the angle of the spiral. The author states that his ob- ject in this inquiry is the application of these elements to a discussion of the hydraulic theory of shells. The constant angle of the spiral, which each particular species affects, being connected by a necessary relation with the economy of the material of the habitation of each, with its stability, and the condition of its buoyancy, it is therefore necessary to determine the value of this angle.

" On the relative attractions of Sulphuric Acid for water, under particular circumstances : with suggestions of means of improving the ordinary process of manufacturing Sulphuric Acid." By Henry Hugh Watson, Esq., Corresponding Member of the Manchester Philosophical Society. Communicated by John Dalton, D.C.L., F.R.S., &c.

The object of the inquiry detailed in the present paper is to determine at what degree of concentration the affinity of sulphuric