No abstract

In mammals the weight of the heart, kidney, lungs, and other organs can be related to total body weight through power laws (allometry). Weights of primate organs are analyzed by this technique. Allometric coefficients and size-independent organ-weight or body-form ratios may be used to compare primates, including humans, and other mammals.

Two sets of quality measures of group care were used to assess their predictive power for two sets of measures of the development of infant and toddlers in group day care. One of the quality measures we investigated was the Early Childhood Environment Rating Scale (ECERS). We replicated the findings of Scarr, Eisenberg, & DealerDeckard (1994) which were that the total score of the ECERS represents a global index and that the 37 items making up the scale are redundant and could be shortened considerably without loss of the scale as a quality criterion of group care for young children. Neither Scarr, Eisenberg, and Dealer-Deckard (1994) nor our own Factor Analyses of the 37 items supported the a priori distinction of seven Subscales. However further findings indicate that regardless of the redundancy within ECERS, two Subscales, dealing mainly with adultchild, child-child and adult-adult interactions, predict the development of infants and toddlers, but only when the measures of development were based on participant observations of the children over a longer period oftime and in the broad context ofthe natural daycare environment. None of the Subscales, nor the total ECERS predicted social development when it was based on precise time sampling observations, assessed by non participant observers, in interactions between a child and a specific caregiver. Such measures ofdevelopment were well predicted in our study by caregiver behaviors assessed through Time Sampling Observations.

Comparison of a small leaf with a large one, or of a child with its parents, leaves the conviction that a "similarity" of some sort is present. It seems reasonable to suppose that an artificial kidney is in some sense physically similar to the natural organ. In order to define biological similarities in a meaningful way it is necessary to review the subject of dimensional analysis, which forms part of the basis for similarity theory.In the past the subject of dimensional analysis was obscured by certain metaphysical overtones; it is still passed over briefly in many technical courses. However, a number of distinguished physical scientists such as Newton (1), Fourier (2), Lord Rayleigh (3), and P. W. Bridgman (4) recognized the importance of similarity and dimensional methods. The basic concept of "similitude" was known to the ancient Greek mathematicians in connection with geometric problems and was noted by Galileo in 1638 (5), during a discussion of structural scale-up problems.During the last few decades dimensional and similarity analysis have been put on a perfectly firm mathematical footing. The method has been applied to all types of engineering problems (6), to theoretical hydrodynamics (7), to heat flow (8), to jet flows (9), to chemical engineering (10), to magnetohydrodynamics (11), to rheology (12), to meteorology (13), and in numerous other situations. General discussions of the method are also given by Duncan (14), Focken (15), and others. From the mathematical viewpoint, similarity has been approached from several different viewpoints: geometric transforThe author is a medical researcher associated with the department of mathematics, Oregon State University, Corvallis, and with the Oregon Regional Primate Research Center, Beaverton. 20 JULY 1962 mations, group theory applied to equations, and finally the algebra of the dimensional symbols (M, L, T, and so on).The geometric viewpoint is illustrated by the fact that two triangles are similar when there is a constant ratio relating their sides. In such triangles one may then define a scale ratio:where Z' is the new length, I is the original length, and kL is the numerical scaling coefficient. It can then be easily shown that kL is no other than the L symbol, which appears when one transforms each variable in an equation by some linear coefficient. The physical sense of this substitution is that the given equation must be invariant for arbitrary choice or change of scales of measurement. It would certainly not be desirable if Newton's laws held in English units but not in metric ones. The fact that physically meaningful equations must be dimensionally consistent was recognized in 1823 by Fourier, but is given surprisingly casual attention in most scientific curricula. A derivation of dimensionless numbers based on scale transformations is also provided by Decius (16). Substituting a transformed variable for the original one in an equation is a very general method which leads to the theory of groups connected with solutions of equations. The matter is a...