PERMANENT WAVING OF HUMAN HAIR: THE COLD PROCESS 113 sections is wrapped around a plastic rod. The diameter of these rods may vary from 1/8 in. to •/8 in. or more. A little reflection will prove that the diameter 0f the rod may in- fluence the type of undulations pro- duced in the permanent waving process, taking into consideration, of course, the fact that as the hair is wound around the rod the effective diameter will increase with each turn and the curvacure will de- crease. In terms of the strain intro- duced in .the individual hair fibers, or rather the differential strain be- tween the inner and outer periphery strength of preparations now in use commercially may vary from about 0.4 N to 0.9 N with respect to am- monium thioglycolate as determined iodimetrically. The pH of these solutions may vary from 9.0-9.5. Usually the alkalinity of the solu- tion is brought about by the addi- tion of ammonium hydroxide. In view of the fact that the system ammonium thioglycolate-ammo- nium hydroxide is a fairly efficient buffer, considerable variations in 'concentration of free ammonia will produce only small changes in the pH of the system. Hence,.it would p_f_ •a_ch__•b_e_r•, _Ta_b_l•__l__lj_s•s•_some seem more desirable to express the. interesting calculations. - the normality of free ammonia % Differential Diameter Extension (Inner Periphery Fiber Diameter Wrapped Fiber), In. 0.001 In. 0.005 In. 0.125 1 .ø60 8.00 0. 250 0.80 4.00 0.500 0.40 2.00 ß These data indicate that the per cent differential elongation is in- ver•ely p.roportional to the diameter of the curvature, either of rod or of rod plus hair if more than one turn of hair is placed around the rod, and directly proportional to the diameter of the hair fiber. (The above considerations show that the physical process of wrapping does or can influence the subsequent wave pattern.) In the systems of cold waving as currently practiced, the waving lo- tion is applied to the hair before it is wrapped around the rod. The rather than in terms of pH. Bases other than ammonia may be used, but at present ammonium hydrox- ide seems to be preferred in corn- mercia.1 waving lotions. It is obvious that ifi order to pro- duce a chemical reaction within the hair fiber we must introduce the chemical agent into the fiber. Speak- ing in practical terms, the degree of alteration or reduction of hair in the cold wave process depends upon the amount of thioglycolate which diffuses into the hair and upon the rate with which this is accomplished. The amount of thioglycolate which is available for diffusion into a hair fiber is a function of the capillary air space between the fibers wrapped around •he rod during a waving process. In Fig. 8 is shown a diagram of a cross section of a tress of fibers in close packed relationship. In the

114 JOURNAL OF THE SOCIETY OF COSMETIC CHEMISTS particular case illustrated, hair fibers of uniform diameter are assumed to form a rectangle (RSTU) with one side equivalent to a total of two hair fiber diameters (2D,. Due to close packing the second dimen- sion is somewhat less than thik amount, and it can be shown readily that it is equivalent to x/• (D,. Therefore the area of the rectangle RSTUequals At = 2(D•) X x/• (D•) Since the equivalent of four fibers is inscribed in this rectangle the cross-sectional area of these hair fibers is given by the expression: At' = •r(D•) 2 The ratio of the area of the rectangle to the area of the fibers included within the rectangle is given by the following equation: At _ 2x/•(D•) '• 2x/õ = 1.i (1) At' •r(D_u) • •r It can readily be visualized that a tress of hair is made up of n rec- tar•gles, each containing four fibers.. 1 R $ Figure 8 Introducing n in equation 1, it will be found that it appears both in the numerator and denominator and hence will cancel out. Equation 1 is therefore of general nature, ap- plicable to any number of fibers. A consideration of the equation for the value of z/' indicates that in a given cross-sectional area this value must remain constant regardless of fiber diameter. If this be true then it follows th•tt the volume of air space must also remain constant. In any tress of hair therefore, the capacity of the curl for permanent wavihg lotion--if it is assumed that all air will be dispelled--is constant. Assigning the term N to the total number of hair fibers in any cross section, the following relationship is arrived at: At' N •r(D•/2) = (2) where z/' eqt•als the cross-sectional' area of the hair fibers and DH equals the diahaeter of each fiber. A relatiorlship between the reac- tive keratin surface ($) in terms of N, L (length of fibers) and DH may then be established by the.follov•ihg equation: 8= •rD•XLX N (3) ß Inasmuch as the value for Nvaries in- versely with the square of the radius of the hair fibers, it will be seen that the reactive keratin surface in a tress will be profoundly affected by the fiber diameter. For example, if the hair diameter is doubled, the number of fibers in a given cross section will be reduced to one-fourth the previous numbers. Accordingly