A large part of the branching vasculature of the mammalian circulatory and respiratory systems obeys Murray's law, which states that the cube of the radius of a parent vessel equals the sum of the cubes of the radii of the daughters. Where this law is obeyed, a functional relationship exists between vessel radius and volumetric flow, average linear velocity of flow, velocity profile, vessel-wall shear stress, Reynolds number, and pressure gradient in individual vessels. In homogeneous, full-flow sets of vessels, a relation is also established between vessel radius and the conductance, resistance, and cross- sectional area of a full-flow set.

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Pepsin. This was Armour salt-free material. Papain. This was twice-crystallized from crude papain (British Drug Houses Ltd.) by the method of Kimmel & Smith (1954). Stock solutions were made by dissolving freeze-dried material to 1 g./100 ml. in 0-0453M-Na2HPO4-0-0213M-KH,PO4 buffer (pH 7-0). In some of the experiments a sample of papain obtained from Schering A. G., Berlin, and of about the same activity as that mentioned above, was used in the same manner. We are also indebted to Mr C. F. Phelps for a sample also prepared by the method of Kimmel & Smith. Ox-serum albumin. This was from material isolated by Dr B. S. Blumberg (Blumberg & Ogston, 1957a). Ethylenediaminetetra-acetic acid. (Hereafter denoted by EDTA.) The same sample was used as that used by Blumberg & Ogston (1957 a). Ethylene glycol bis-(f-aminoethyl ether)-NN-tetra-acetic acid. (Hereafter denoted by EGTA.