CORRELATION OF THE VOLUMES AND SURFACES OF ORGANISMS. It has been pointed out by Leuck art and by Herbert Spencer that as organized unicellular bodies increase in bulk, their sur faces become proportionately less, and that this elementary rule of growth very probably leads to the necessity for segmentation or subdivision of the original cellular body, "owing to the un favorable conditions. which continuous growth establishes between the organism and its sur roundings, thus developing unfavorable conditions for nutrition, respiration, and consequently for metabolism and growth in general." (Ryder.) But, as Ryder claims, there are "supplementary host equally important principles connected with the geometrical ratios with which the forces of growth, reproduction, and metabolism are simul taneously operative during the development, growth, and evolution of organic types"; and he claims that "without resort to another type or set of adjustments which living beings have effected in relation to the outer world, the pres ent development of organized resistance, and even of animal motion and mentality, would in all probability have been an impossibility." The primary form of living beings, as the low est plants and animals, is that of a sphere, the spherical shape being due to gravity and surface tension. But Ryder points out that this shape is one "which is itself unfavorable for growth, with a proportionate and concomitant acquisition of new surface, since of all forms of bodies it is the very one which can contain the greatest amount of matter within the least amount of surface." Hence any departure from this primitive spheri cal form "will increase the proportional amount of enveloping surface in respect to the volume of enveloped matter." Hence, first, the tendency of organs to extend indefinitely in the form of a cylinder, with rounded or hemispherical ends, which becomes more and more attenuated as its length is increased, as in the nerves, or blood vessels: and, secondly, the formation of flattened disk-like bodies, such as the blood-corpuscles.
Why do the nerves, blood-vessels, etc., grow slender and branched? Ryder answers this ques tion by saying that the indefinite stretching or flattening of a mass achieves the same thing "as splitting it up into a great many slender bars, and placing these end to end, or, as splitting up the mass into a great many thin slices, and join ing these edge to edge. In both cases a great gain of surface is accomplished. Now if a body branches rapidly, it does the same thing as is done when it is split up into a great many slender bars; namely, it increases its surface in a ratio corresponding exactly to the rate at which the splitting or branching takes place." This is what the vascular system has done. The branching of the blood-vessels, with their in numerable ramifications, "is nothing more than a physiological response, developed in a geometri cal ratio, to a correspondingly rapid increase in the volume of the organized matter to be metabolized." So with the nervous system, "the extreme attenuation of the terminal and central interrelative fibres given off by the ganglion cells of the nervous system means a gain of sur face in proportion to mass which is nowhere else paralleled by any active constituent tissue of animal bodies." The enormous development of the irritable surface is, he adds, correlated with the extreme irritability of the nervous system. This is exemplified by the tenacity of the nerve ter minals of the auditory organs and the other organs of sense; while it is the most attenuated structures known to the histologist which are the most irritable, as cilia, flagella, etc. This subject is further illustrated by the stretching of plasma into threads, as the pseudopods of many protozoans, the branches and filaments or flattened leaf-like forms of gills, as well as the roots and branches of plants. Thus organisms higher than spherical protozoa have, after life began, proceeded, during their growth in volume, to develop surfaces according to this rule of geometrical progression.