On Volume in Biology

Abstract

of quadratojugals, dermosupraoccipitals and tabulars has been defi-nitely determined, and the supratemporals almost as definitely, thus giving to the genus nearly every skull element found in the most prim-itive cotylosaurs. The mandibles may be a little less slender and there may be fewer teeth but one can say with assurance that were an isolated skull of Sphenacodon found in Texas it would be referred unhesitat-ingly to Dimetrodon. And this similarity extends to other parts of the skeleton, with the exception of the spines of the vertebrae. Many and various have been the conjectures offered to explain the extraordinary spines in Dimetrodon. In my opinion nothing better has been suggested than that of Professor Case, namely, that they repre-sent an ornamental or senile character of the race, of no profound im-portance in the life economy of the animals. Certainly, as I have pre-viously observed, if the spines of Dimetrodon had been of important use to their possessors they must have produced correlated differences in other parts of the skeleton. The differences in the spines have no more than a generic value. There are doubtless several species of Sphenacodon in the New Mex-ican beds, but the known remains from the Baldwin and Miller bone-beds seem all to belong to one species. From different horizons on the Puerco, however, large specimens are known, now preserved in the Yale Museum. The present specimen, which doubtless belongs to S. ferox Marsh, was nearly five feet long as figured. The Yale speci-mens indicate a form one-half larger, or about seven and a half feet in length, or of about the size of most specimens referred to Dimetrodon incisivus. Sphenacodon is definitely known only from the valley of the Puerco and its tributaries in New Mexico; not a fragment of it has been found in the El Cobre deposits scarcely a score of miles away. How-ever, there are specimens in the Chicago collection from Texas that suggest very strongly its occurrence there, but definite proof is lacking. In one respect this subject is time-honored. Herbert Spencer and many others since his day have recognized the biological importance of the principle of similitude. Bulk increases as the cube of length; surface as the square. Hence the limitation of the size of cells, the, 654 BIOLOGY: L. J. HENDERSON minute canalization of the body, and the prodigious jumps of the flea, as well as the variation in metabolism with the size of the organism. Yet even this subject is by no means exhausted. For example (a fact which appears to be of some importance in describing the internal regulation of temperature) the difference in temperature between center and surface of a sphere which is producing heat uniformly throughout its whole mass, when equilibrium has been established with a sur-rounding liquid medium of constant temperature, is proportional to the square of the radius.1 But apart from this great principle and certain superficial discussions of the nature of oedema and similar phenomena, the regulation of vol-ume has remained without any physico-chemical analysis. Yet, from the standpoint of physical science, this is perhaps the most universal and fundamental of all organic regulations. I believe that this strange neglect may be traced to three facts. In the first place, the chemist is accustomed to vary the volume of his systems to suit his convenience. This is a justifiable practice, because, if the phases are so large that capillary phenomena may be disregarded, and so small that gravity need not be taken into account, the division of a phase into two parts does not change its energy. Thus, volume hardly enters into our cal-culations except as an indirect expression for that which is regarded as the true variable, viz., concentration. This, however, is to disregard the real question as it presents itself in biology. Secondly, when equilib-rium has been established in a heterogeneous system, as Willard Gibbs rigorously proved, the volume of the phases-capillary and gravitational phenomena being absent-is not relevant to the state of the system. But it may be at once observed, first, that until equilibrium has been attained the volume is of great moment, and, secondly, that equi-librium is never attained within the organism. Finally, the ordinary conception of the process of diffusion is based upon a mathematical discussion, which, though leading to a consistent description of the phenomena, is nevertheless a false representation of the actual occur-rences. And nearly all physiological changes of volume depend upon diffusion.