EVALUATION OF ANTIPERSPIRANT ACTIVITV 751 MATHEMATICAL CONSIDERATIONS When one wishes to compare the effectiveness of antiperspirant mate- rials, it is obvious that tests must be performed directly on human sub- jects. However, people perspire for many reasons other than too high a temperature or humidity. Many other factors, such as emotion, tem- perament, and other psychological stimuli, state of health, variation of diet, etc., also influence the degree of perspiration (15). Control of all these variables simultaneously and from test to test is totally impossible. For this reason a single x to x' comparison, in which the output of per- 4 7 Figure oe. Plots of perspiration output of area A rs. area B for different types of control tests spiration, x, from one area, A, of the body is compared to x' from the same area of the body after a product has been applied, cannot be made with accuracy. There is no way of knowing how much of an influence these variables may have had on the change in the value of x to x' as opposed to the influence of the test product coincidentally applied. In order to obtain a value for x' which represents an antiperspirant effect free of these variables, it has become standard practice to measure the output from another area, B, simultaneously with that from area A, as originally proposed by Fredell and Read (5). The ratio of perspira- tion between the two areas may be defined as x/y, where x is the value

752 JOURNAL OF THE SOCIETY OF COSMETIC CHEMISTS obtained from area A and y is the value from area B. This test is done once with no product applied to either area. The ratio itself becomes the control. In a second test an antiperspirant material is applied to area A, leaving area B untreated. If the material is effective, a lower perspira- tion rate will be obtained from area A, to which a new value x' is as- iii/ I IIIII / 11 / •/•ontro, / // X •'• Values for Area A Figure $. Practical plot of the output of perspiration from area A & B under control and test conditions. The dotted lines rep- resent the corrected test lines for a valid comparison signed. The output from area B may increase or decrease, but rarely will it be the same as that of the first test, because of the influence of the uncontrollable variables. The value y' is assigned to it. The result of the second test is a new ratio of perspiration from the two areas for the condition where a product is applied to one side only. It is expressed as x'/y'. However, x' includes both the effects of the product and those of the uncontrollable factors which caused y to change to y'. Thus the following inequality results: x ! 0c y•y A new value of x from area A, which does not include the effects of the product when y' is the value for area B, is now required. It may be cal-