Studies in the physicomathematical theory of organic form

In continuation of previous studies the theory is developed on the assumption that the form of any organism is determined by requirements to perform definite biological functions. A previously outlined theory of the form of plants is developed further, showing how the conditions of mechanical strength together with the specifications of the total mass and metabolism, may quantitatively determine not only the general form of the plant, but even the number, size, shape and shades of the leaves. Next the form of animals, as required by mechanical conditions and by the different types of possible locomotions is discussed. A mathematical theory of locomotion of snakes in relation to their shape is outlined. Next is discussed the form and locomotion of quadrupeds. A number of theoretical relations, which describe the shape of an animal, are derived and compared to available observations. After that the theory of flight of birds and insects is discussed, and again some form relations comparable with observations, are discussed. Finally a set of equations is outlined, which determines not only the external shape, but also the internal structure of animals. Different relations pertaining to some inner organs are derived and compared with available observations. The paper ends with a brief discussion on the shape of unicellular organisms.