fications of the aggregate to which they belong. They undergo the influence of the environment, though indirectly, through this aggregate. Their modifications are new directions, amplitudes of new vibrations, which place them in equilibrium with the forces which the ensemble of the aggregate, as modified by the environment, brings to bear upon them. These modifications endure as long as equilibrium endures, and are ever transmitted to the new units which spring from the former ones, until, on the equilibrium being disturbed, a new breaking-up of the existing relations necessitates others.
The hypothesis of physiological units is a necessity, not only in order to fill up the gap which separates the highest products of organic chemistry from those irreducible elements revealed by the microscope which we call morphological elements, but also in order to furnish a substratum for the positive property which serves to account for the great facts of biology, and to refer them, by formulæ expressed in terms of mechanics, to first principles.
Let us now consider the great facts of biology.
The growth of an organism is an operation essentially like the growth of a crystal. "Around a plant there exist certain elements that are like the elements which form its substance; and its increase of size is effected by continually integrating those surrounding like elements with itself. Nor does the animal fundamentally differ in this respect from the plant or the crystal. Its food is a portion of the environing matter that contains some compound atoms like some of the compound atoms constituting its tissues; and, either through simple inhibition or through digestion, the animal eventually integrates with itself units like those of which it is built up, and leaves behind unlike units."
Organic growth differs from inorganic in this, that it has limits. All conditions remaining the same (a proviso that must always be made in biology), and the quantity of integrated substance not varying, we find that, by the principle of the persistence of force, the growth of the living being must depend on the expenditure. The only portion of the integrated substance that can serve for growth is the unexpended residue, the excess of nutrition over expenditure—a quantity which is essentially variable, and which transfers its variations to the growth, limiting it and diminishing it more or less rapidly from the moment when the body of the living thing has attained its full development. Experience shows that the limit of growth is fixed for those organisms which have large expenditure, and that for those which have hardly any expenditure this limit gradually recedes; of this the crocodile is an instance. But there is another element which must be taken into account, namely, that the definitive volume of an organism, being the sum of its initial volume and of its successive increments, must depend upon the initial volume. The definitive vol-
