574 JOURNAL OF THE SOCIETY OF COSMETIC CHEMISTS torsional stiffness of beams increase with the fourth power of the diameter, as is shown by equations (1) and (9.): C1 0 = k --- (•.) M r 4 where 0 equals twist k equals numerical constant C equals force couple 1 equals length of beam M equals modulus of rigidity and r equals radius of beam. The theoretical value of a sixteen-fold increase in body with a two-fold in- crease in diameter has been measured by us on certain fiber arrays. This fac- tor is one of the most important in determining natural hair body, both by the visual and tactile methods, because the fiber diameter variation is significant among individuals. Again, carpets provide a descriptive example for this characteristic: fine merino wool is rather unsuited for carpet making in con- trast to a coarse South African wool. For equivalent compressire strength and resiliency of a carpet, more wool-by weight-of the former than of the latter type is needed. 4. Fiber configuration: The term fiber configuration primarily refers to curliness versus straightness and, secondly, to the array of the fibers. To some extent, the angle of hair fibers relative to the skin belongs to this category. Curly or crimped fibers increase the bulk volume of a fiber assembly that is, they provide stabilized structures at lower density. An appropriate example is that all bulky knit fabrics rely on crimped fibers. In the case of wool, the crimp is natural, while for continuous filament synthetic fibers, it has to be processed into the yarns separately. Two basic factors are operational vhen the stabilized bulkiness of a fiber mass is due to curl. One is that a curved object creates a prohibited space-larger than its own material volume-which other bodies cannot easily enter. Secondly, curved fibers establish contacts with larger numbers of neighboring fibers than straight ones. An extreme ex- ample for curl induced bulkiness and resilient strength in hair is the nahlral or Afro style. This cannot be achieved with straight hair without resorting to other stabilizing treatments. 5. Fiber-fiber interactions: The last major factor is the surface interaction between fibers, which determines the ease or difficulty of fiber displacement within the mass structure. The structural strength of any multicomponent sys- tem, and, therefore, the body of a hair mass, depends on the effective stabili- zation of the component units relative to each other. When applied to hair, this overall parameter includes a number of basic factors: material frictional characteristics and surface roughness of the fibers themselves, lubricity, shear resistance, and the adhesiveness of any surface coatings under the static and dynamic conditions operating on a hair mass. It is safe to state that the stron- ger the surface interaction between contacting fibers, the higher the hair body.

HAIR BODY 575 In our view, the concept of hair body, as defined above, is exhaustively described by these five variables. The variables are causatively independent of each other, but synergism can exist. For example, fibers of higher material moduli or larger diameter can enhance the structure stabilization by surface interaction as well, because they are able to support higher normal forces. This, in turn, results in greater frictional iramobilization. According to the above given interpretation of hair body, none of the five variables have exclusive influence on the overall behavior. Therefore, any specified level of body, if a quantitative scale existed, could be obtained by a nearly infinite number of variations among the five factors. Obviously, when a given bo.dy level is achieved by different combinations of the fundamental parameters-for instance, a decreasing fiber diameter is balanced by increas- ing hair density-some other perceptible hair mass characteristics will change. These changes, however, belong to second-order behavior patterns, specifical- ly to texture qualities. C. Cosmetic Products and Hair Body The specific influence of cosmetics on hair body is best discussed by analyzing the changes in the five basic parameters caused by different cosmetic products. It may be stated summarily that cosmetics-according to the current defini- tion of the term-cannot directly influence any of the five parameters so far as the biological synthesis of the fibers is concerned. Compositions or treat- ments which could grow denser, stronger, thicker, curlier, or rougher hair would be outside the field of cosmetics. Therefore, the discussion needs to involve only those effects of cosmetics which occur on grown hair. Cosmetic products can have only indirect and/or negative effects on fiber density. The on-head fiber number can be considered as a kinetic equilibrium determined by the rate of new fiber growth on the one hand and the rate of fiber elimination on the other. As mentioned above, fiber growth rate is not a cosmetically solvable problem. The rate of fiber attriti.on, however, can be influenced to some degree. Treatments or products, which result in more difficult combing, accelerate the rate of fiber elimination, thereby reducing the fiber density to a lower steady-state level. Lubricants, on the other hand, de- lay the mechanical fiber removal and assist in the maintenance of marginally higher fiber densities. Nonetheless, these effects are secondary, and it may be stated that cosmetics do. not significantly influence hair body through modi- fication of the fiber density on the scalp. The modulus or stiffness of polymeric materials can be increased by chemi- cal treatments. This has been achieved on natural fibers, including keratin fibers, by cross-linking, or by introducing bulky side groups. However, the nature of the reactants and/or the reaction conditions are such that, at pres- ent, these methods cannot be used for on-head treatments. No current cos- metic products increase body by this method. Conversely, some cosmetic