742 JOURNAL OF THE SOCIETY OF COSMETIC CHEMISTS It can be added, finally, that these five standard defects are not formed independently of each other but can appear simultaneously, thus further complicating the problem. The remedies suggested where surface defects are traceable to the fatty base itself (cases 3, 4, and 5) are not commercially feasible because they require major changes in installations. The problem can, however, be solved more easily during the study of new formulations. It would, therefore, be useful to ascertain rapidly whether surface defects are formed readily by the chosen fatty base. For that purpose, it is sufficient to place the suppository in a thermostat at a temperature at which the suppository is slightly softened. Under these conditions, surface defects almost always appear after a few days. If these are fine, homogeneous and visible only under the microscope, they are not serious, and the suppositories can be manufactured according to the chosen formula. On the other hand, if surface defects are formed which are visible to the naked eye, it would be better to seek another suppository base. (Received June 24, 1964) REFERENCES (1) Whymper, R., in W. Andersson, Rev. Intern. Chocotat., 18, 2 (1963). (2) Reinders, W., Doppler, C. L., and Oberg, E. L., Rec. Tray. Chim. LI, 917 (1932). (3) Becker, K., Fette, Seifen, Alnxtrichmitte[, 59, 636 (1957). (4) Kleinert, J., Rev. Intern. Chocolat., 16, 345 (1961). (5) Vaeck, S. V., Ibid., 16, 490 (1961). (6) Giddey and Clerc, Ibid., 16, 530 (1961). (7) Andersson, W., Ibid., 18, 49 (1963). (8) Lutton, E. S., •7. zfm. Oil Chemists' Soc., 27, 277 (1950). (9) Sambuc, E., and Naudet, M., Rev. Franc. Corps Gras, 1, 10, 17 (1959). (10) Mahler, E., Bull. Tech. Gattefoss•, 56, 49 (1958). (11) Mahler, E., Ibid., 55, 58 (1957). APPENDIX I. Raw Materials Codex cocoa butter is cocoa butter meeting the specifications of the Codex Pharmaceutique Frangais. Printex U carbon black is obtained from Degussa, Frankfurt, Germany. Suppocire .4 is an interesterified hydrogenated palm oil having a melting point of 35ø-36øC. It is marketed by Gattefoss&sfpa, 15 rue Constant, Lyon (35) France. Suppocire C is similar to Suppocire A but contains more of the higher molecular weight fatty acids. It melts at 38øC-40øC. It is marketed by Gattefoss&sfpa. Suppocire L is hydrogenareal oil interesterified in the presence of poly- oxyethylene glycol. It melts at 38øC--39øC. It is marketed by Gatte- foss?c-s fpa.

THE STUDY OF SURFACE ANOMALIES OF FATTY SUBSTANCES 743 Suppocire BS2X is an interesterified hydrogenated palm oil combined with fatty acid esters of polyoxyethylene. It is marketed by Gattefoss•- sfpao APPENDIX II. Examination of the final portion of the curves of dilatometry at constant temperature shows that the time values and the expansion values con- stituted a series proportional to the series x 1 2 4 8 ... 2 • of general terms xn = 2 • and y• = •n, which are linked by the hyperbolic relation yn = lx•. In a system of orthonormal axes, this yields an equi- lateral hyperbola. The part of this hyperbola which is relevant corresponds to x 0 and y 0, i.e., the branch asymptotic to time. The other pairs of series pro- portional to x• and y• have other equilateral hyperbolas as graphs which can be considered as resulting from the use of other unit vectors, corresponding to a simple point-by-point transformation represented by a matrix one obtains, for example, graph G2 from graph G• (cf. Fig. 27), through the matrix transformation It may be recalled that such a transformation leaves the symmetry of the curve invariant in relation to the bisector of the axes. A simple geometric property of the hyperbola enables one to determine the asymptote to time from the experimental graph. Consider points M (1, 1) and P (2, •/•) be- longing to (G0. coM is the bisector of orthonormal reference aingle cox, coy, and tangent T at Mhas a slope of -45 ø. Let •be the projection of M on cox and N the projection of P on •M. In triangle MNP, MN = • and NP = 1. Angle NMP is equal to % the tan of which is 2. This also applies to triangle NoOP. (Similarly, in the case of G2, point •' is the pro- jection of M' on cox.) The determination of the asymptote cox is then carried out as follows: M is found as the point through which tangent Tpasses with its slope -45 ø (this is relatively easy if the curve is plotted on graph paper. The posi- tion of point M is obviously approximate). From point M, a vertical line Mm is drawn parallel to the ordinate and a half-line Mp is constructed which forms an angle • with Mm, so that tan g = 2. This half-line meets the experimental curve at P. N is found as