A new principle is derived from mathematical considerations which will allow the calculation of the number of bodies contained in the unit volume by counting the number of transections on the unit area of a random section. The simple equation involves two coefficients related to the volumetric density of the bodies in the volume, and to their configuration. Means for the accurate determination of these coefficients are given. The verification of this principle in model experiments showed a high degree of reliability of the method with average errors of estimate of 2–4%. The method has been applied to the counting of alveoli in five normal human lungs, which were found to number an average of 300 million, with a striking constancy from lung to lung. Submitted on May 31, 1961

An attempt has been made to define quantitatively the architecture of airways and blood vessels of the human lung. For this purpose five normal lungs from individuals aged 8 to 74 years were subjected to a dimensional analysis by several methods of measurement based on statistical principles. The elements of the "respiratory zone" may be regarded as randomly distributed in the lung. There are essentially the same number of alveoli (300 million), alveolar ducts (14 million), and capillary segments (280 billion) in all lungs. The dimensions of these architectural elements are shown to depend mainly on the size of the lung. The effect on these dimensions of such functional variables as the degree of inflation of the lung or of the filling of capillaries with blood are discussed. The alveolar and alveolar-capillary surface areas, which are of importance in the analysis of gas exchange between air and blood, are found to increase with the size of the lung. In our material, both varied in the range of 40 to 80 square meters. The elements of the conductive zone of the lung show a polar orientation. The airways have, on the average, 23 generations of dichotomous branching; the pulmonary arteries reach the precapillaries after about 28 generations. The average diameters of the airway and blood-vessel elements at each generation appear to follow the laws of "best" dimensions. The functional significance of this finding is discussed. It is suggested that morphometric studies conducted according to this general model may be useful in the anatomical description of other organs (16).