STATISTICAL APPROACH TO COMMON VARIABLES 447 The extent to which preparative variables are important for stability of the emulsion made from the emulsifiers and oils studied is indicated in Table 8 for o/w emulsions and in Table 9 for w/o emulsions. In these tables is listed, for each preparative variable, the level of the experimental design showing significance in addition, the number of emulsifier-oil pairs for each oil exhibiting significance at this level is shown. In the case of o/w emulsions, it is evident that higher emulsifier concentration (2.5 per cent), higher concentration of water (90 per cent) and higher temperature (70øC.) appear to be of importance in conferring stability on mineral oil, cottonseed oil and oleic acid o/w emulsions. Addition of oil to water, under the conditions used, was less frequently of importance to the forma- tion of stable o/w emulsions. Although placing the surfactant in water as opposed to oil is favored in the case of mineral oil, this factor is less important or nonexistent for the other nonaqueous liquids. Agitation by means of the Homo-Mixer instead of by propeller appears to be of value with mineral oil. The number of significant factors is appreciably less with methylphenyl silicone than with the other three oils. It may be con- cluded for the range of emulsifiers tested that the chemical or physical nature of this oil primarily determines the stability of its emulsions. Few preparative factors were found to be important for the stability of w/o emulsions. Of the 42 emulsifier-oil pairs which formed at least one w/o emulsion, there are 252 emulsifier-oil-variable comparisons possi- ble only 20 were found to be significant. A small proportion of water TABLE 8--FREO. UENCY OF VARIABLE LEVELS SIGNIFICANTLY FAVORING STABILITY OF O/W EMULSIONS (90-30) Emulsifier Water, Emulsifier Temp., Order of Oil Conc., % % Location øC. Addition Agitation 2.5 (6) 90 (6) w (4) 70 (7) o -+ w (4) H (5) o (1) P (1) 2.5 (6) 90 (3) o (1) 70 (5) o --• w (2) H (1) 30 (1) 2.5 (6) 90 (4) w (1) 70 (4) o-• w (3) H (2) o (2) 25 (1) 2. $ (2) 90 (1) w (1) 70 (2) o • w (1) H (1) 30 (1) o (1) Mineral Oil Cottonseed Oil Oleic Acid Methylphenyl Silicone Frequencies of significant levels are shown in parentheses. TABLE 9--FREO. UENCY OF VARIABLE LEVELS SIGNIFICANTLY FAVORING STABILrrY OF W/O EMULSIONS (90-30) Emulsifier Water, Emulsifier Temp., Order of Oil Conc. % Location øC. Addition Agitation Mineral Oil 30 (4) Cottonseed Oil 30 (1) Oleic Acid 30 (6) 25 (2) w -* o (2) Methylphenyl Silicone 30 (3) 25 (1) w --• o (1) Frequencies of significant levels are shown in parentheses.

448 JOURNAL OF THE SOCIETY OF COSMETIC CHEMISTS (30 per cent) appears as a significant factor at least once for each oil. With oleic acid and methylphenyl silicone, a low preparation temperature (25øC.) and addition of water to oil were found to be significant in a few cases. Thus, with w/o emulsions as compared to o/w the chemical and physical nature of the oil and emulsifier is even more important than pre- parative variables in determining stability. In summary, within the limits studied, the results of the statistically designed experiment applied to four oils and thirteen surfactants have confirmed the previously known importance of a high proportion of water in making stable o/w emulsions and a small proportion of water in making w/o emulsions. Of discernible, but lesser, significance to emulsion type and stability is the addition order adding oil to water yields the expected o/w emulsion. Higher levels of emulsifier concentration and a higher preparative temperature are important in conferring stability on o/w emul- sions. Emulsifier location and, within the experimental limits studied, method of agitation do not exhibit consistent significance. In a large number of the emulsifier-oil pairs studied, particularly those forming w/o emulsions, none of the individual preparative variables showed significance in determining stability. It is evident that the chemical and physical nature of particular emulsifiers and oils in combination have a major influence on the type and stability of emulsions which are formed. Acknowledgment: The authors wish to express their appreciation to B. N. Baer, A. N. Green, A.M. Levine, R. D. Charles and P. Becher for their several contributions to this study. (Received May 8, 1962) REFERENCES (1) Becher, P., "Emulsions: Theory and Practice," ACS Monograph No. 135, New York, Reinhold Publishing Corp. (1957), pp. 209-244. (2) Becher, P., 7. Soc. Cosmetic Chemists, 9, 141 (1958). (3) Becher, P., Ibid., 11, 325 (1960). (4) Davies, O. L., "Design and Analysis of Industrial Experiments," London, Oliver and Boyd (1954), pp. 484485. (5) Griffin, W. C., in "Encyclopedia of Chemical Technology," Vol. 5, New York, The Inter- science Encyclopedia, Inc. (1950), pp. 692-718. (6) Griffin, W. C., and Behrens, R. W., Anal Chem., 24, 1076 (1952). (7) Ross, S., Chen, E. S., Becher, P., and Ranauto, H. J., 7. Phys. Chem., 63, 1681 (1959).