Abstract
The application of dimensional analysis in biology is further illustrated by functional equations composed of dimensionless numbers and dealing with renal physiology, lung physiology and plant leaf shape. Dimensional variables and dimensionless numbers are examined from the viewpoint of numerical invariant properties of a certain physical system. Utilization of the method for problems such as design of an artificial kidney is considered briefly. A tabulation of variables useful in biology is given, with suggestions for a number of new dimensional entities. A continuation of the list of dimensionless invariants from Part I (Bull. Math. Biophysics,23, 355–376, 1961) is provided and includes terms pertaining to general physiology, geometric growth, metabolism, ecological interactions, muscle kinetics and other areas. It is pointed out that use of dimensionless ratios (similarity criteria) makes possible a direct comparison of form or shape factors and relative growth ratios with a variety of physical ratios, through the use of functional equations containing only dimensionless entities. Organismal similarity during growth and development, and between genetically related species, may be analyzed in terms of “automodel” or “self-similar” systems governed by certain dimensionless invariants. Tables of biological variables and dimensionless groupings are included.
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