involving densitometry, f consists of all substances that have essentially the same density as storage fat (triglycerides), but it is assumed that f includes only such fats. The same criterion necessarily applies to w, p, and m. In particular, water is regarded as pure water and not as body fluids, which are solutions mainly of proteins and inorganic salts and therefore have higher densities. Protein and mineral as expressed by »p and m are the total of these constituents, including these substances in the fluid spaces as well as in cellular matter. In the numerical evaluation of constants in formulas for estimating fat, it is assumed thal the densities of f, w, p, and m are relatively constant compared to other biological factors, and the following values are used here: d, <= 0,900 gm/ce at 37°C da = 0,993 ae a6 ad ae d, sy 1.340 aa oa éd oe ays = 3.000 “a es se aa The studies of Fidanza, Keys, and Anderson cited by Keys and Brozek (1953) indicate remarkable uniformity in the density of human fat irrespective of body site.' Further investigations are needed to establish that human fat density is essentially constant for all individuals. This result, though desirable, would be at variance with observations on melting points of human fat and the density and composition of animal fata, which appear to change somewhat with diet and environment. The reliability of the numerical values of d, and d,, cannot be argued with great confidence. Proteins vary in density, and the value of 1.340 gm/cc ia an average for fully hydrated protein in vitro. Whether or not it is the correct average for human protein in vivo has not been demonstrated. The same reservation applies to d,, = 3.0 as well, and some authorities will prefer 2.9 gm/cc. Nearly as fundamental as the three universal relations stated above is the need for a reference body upon which all the methods except that of combined total body water and density are based. For the most part the reference body has been tacitly assumed and often illdefined, but neverthelesa present in every study of body composition. When only one or even two properties, such as water and density, are measured, it is necessary to assume that a constant relationship exists among the remaining constituents. In doing so, a reference body is implicitly introduced to which ali individuals are presumed to conform except for differences in the proportion of adipose tissue. The best defined reference bodies have been the “fat-free body,” ' Editors’ Commens (J.B.): See Fidanaa, F. Keys, A. anc Anderaon, J, T., Density of body fat In man and other mammals, J. Appl. PAweiol.. 6, 262-266 (1968). 226 am Behnke’s “lean body mass” (Behnke et al., 1953), and the Minnesota “standard man’ (Keys and Brozek, 1953). Each of these assumes constant relationships between constituents that most indirect methods for estimating body composition cannot in themselves measure. In the first of these concepts it is assumed that all adult normal humans are identical in their ratios of water, protein, and mineral, und that they differ only in possessing varying proportions of pure fat that is appended to the basic fat-free structure. Behnke’s lean body mass is essentially the same thing except for recognizing that the body contains certain essential lipid substances such as phospholipids that are irreducible cellular constituents. The view that the body may be regarded as fat-free structure to which pure fat is added appears to obtain in small mammals and is aupported by some animal studies. The recent studies of Pitts (1956) appeur particularly to support this contention in guines piga, at least in animals for which fat is lesa than 25%of body weight. On the other hand, the extensive studies of Keys and BroZek on changes in body composition in humans during weight changes due to altered diet suggest that adipose tissue——or at least the tissue gained or lost—is not pure fat, but consists of water and cellular material as well. Behnke (1954; Behnke et al., 1953) has reported similar findings, though numerically somewhat different. Keys and Brozek (1953) felt that the fat-free body could not serve as a suitable reference because its composition would depend, in part, on the fatness of the individual. Instead, they adopted a ‘“‘standard (reference) man” derived from the mean composition estimated for a selected group of normal young men. There is not as yet sufficient experimental evidence to formulate precisely what constitutes a satisfactory reference body, nor for that matter to assume that all adult humans must necessarily conform to any one reference. Nevertheless, a reference body is essential to most of the methods discussed here and must be introduced into any generalized formulation for calculating fat from fluid spaces or density. The analysis of each method therefore proceeds from a generalized reference body whose composition is 1—/f, + w, + p.-+m, and whose density ig d,. It is then assumed that other individuals differ only in possessing a greater or smaller proportion of adipose tisaue, A, whose generalized composition is t= f,; + w, + p, + m, with density ds where fi, wi, #1, and m, are the proportions of the constituents in auch tissue. The quantity A is therefore the ‘“‘adipose tissue” difference between a given subject and the reference man in the sense that it was employed by Keys and Brozek but in more general form. The total proportions of fat, water, protein, and mineral in the normally hydrated person are therefore: 226 DISSWID WSTIOGV.LARW NOLLIELIN foo) HAGOLOO HIGWALdAS & ON G TOA NOLLALLOIN V.9.U. LIDTANY