are explained by Geometry. 5 
(1.) Forms of hybernation ; (2.) Forms of development; and 
(3.) Perfected or matured forms. What, then, are the teach- 
ings of geometry with respect to all of these? And first as 
to 
Forms of Hybernation. 
The ambient medium, from some cause or other which is not 
inquired into, is supposed to be unfavourable to the deploy- 
ment of life in it; the form of the orgasm or living being, 
which is the object of thought, is supposed to be as yet unde- 
termined ; and the problem to be solved is supposed to be the 
construction of a form within which life may be best protected 
from the unfavourable action of the ambient medium, and 
best conserved until some favourable change take place in 
this respect, either in the medium where the orgasm is, or in 
the orgasm itself, by change of place. Suppose, for instance, 
that an orgasm or living being (in whose interior liquid water 
is, of course, necessary to the continuance of its life) is to have 
a bed of snow assigned to it as the medium which it is to ani- 
mate. Or suppose an orgasm is to have, as its present abode, 
an ambient medium consisting of the same substances as itself, 
and from which it has just been separated or secreted, andinto - 
which, consequently, it cannot but tend to return by reabsorp- 
tion and aysimilation again, the question is, what form shall be 
assigned to it that shall best protect it from the unfavourable 
condition of the ambient medium, and preserve its being and 
its life till better times? Now, this is a definite problem in 
applied mathematics, and the solution is equally simple and 
explicit. In the circumstances described, an orgasm ought 
obviously to be moulded into that form which exposes the 
smallest number of its parts or particles to the ambient medium, 
and which, consequently, secludes and protects the largest 
number from it. It should obviously be moulded into that 
form which has the smallest surface and the largest interior or 
solidity. Now, whatis this? Geometry finds no difficulty with 
the answer. Plainly it is the sphere. Wherever, therefore, 
the construction or the conservation of orgasms or living forms 
ina medium unfavourable to the deployment of their life is the 
aim of nature, and whether we view nature as the creation of 
Intelligence, or as itself instinct with intelligence, we should 
