EVALUATION OF ANTIPERSPIRANT ACTIVITY 753 culated as x" from the previously determined values x, y, and y' in the following expression: -- =-orx" - (1) If the uncontrollable factors cause y' to be less than y in the control area, then x" will be less than x. If the converse is the result, then x" will be larger than x (see Fig. 1). If the antiperspirant applied has been effective, the calculated value x" from area A, representing the condition of no product applied, will always be larger than x', the value determined from area A representing the condition of a product applied. The following calculation will give the per cent depression of perspiration caused by the product: •O tt __ X t x• ß lO0 = per cent depression (2) This is the mathematics used in previous work to obtain the desired information from antiperspirant test data. However, these calculations were based on the tacit assumption that the ratio of the rates of perspira- tion from two areas on a human body remained constant at all levels of perspiration. Previous work has taken for granted that this assumption is valid however, no direct proof has yet been offered. It is known that human subjects perspire in erratic ways and from many causes other than exercise, heat, and humidity (15). Thus, the constant nature of this ratio becomes of prime importance. If proven to be false, then all previ- ous work becomes quite inconclusive. In part this paper will prove the validity of the original assumption and that previous work, based on the calculations just discussed, has contained unexpected errors which have compromised the results. A graphic representation of these calculations compared to the graphic treatment of data by the proposed procedure will clarify these errors and demonstrate a means for separating them from the desired information. The graph in Fig. 1 presents the relationship of the perspiration values obtained from area A as plotted against those from area B. Point a is the specific ratio, x/y, obtained for the values x and y derived from the simultaneous test of areas A and B respectively. Because the perspira- tion rates from the right and left axilla of a given individual are rarely equal, these values will seldom be the same. Line 1 drawn through point a to the origin of the graph represents, as assumed, a set of equal ratios for the values obtained from areas A and B for various rates of perspiration in the condition where no product is applied to either area.

754 JOURNAL OF THE SOCIETY OF COSMETIC CHEMISTS G•s Cylinder O/ Wet 9•s valve X X • • 0 (-Højs•ur'zer J • Mixin 9 Chamber Ri9h% Lef[ Cup Cup He• Chc•mber H a. nomeber- Flow ois•ure Honi•or• o Left• ,.Side o F__lect:ric X-Y Recorder Figure 4. Diagram of equipment organization Point b, the ratio x'/y', represents the new ratio obtained from a second test in the condition where a product is applied to area A only. Similarly, line 2 through point b to the origin of the graph is a new set of equal ratios, but in the second condition. The value x" is obtained by extending a horizontal line from point y' through b to the intersection c on line 1 and dropping a perpendicular from c to the x-axis. Now two perspiration rates, x' with product and x" without product, have been established for area A while the value for area B is unchanged, i.e., equal to y'. These two values of x may now be used to calculate the per cent depression of perspiration as described previously (eq. 2). This treatment of data, whether graphic or calculated, is valid only if the ratios in each set are constant at different perspiration rates, i.e., the lines on the graph representing them pass through the origin. Assume that point b had fallen instead on a line such as 3, not passing through the origin. With this single point there is no way of knowing which way the ratio line is directed. As a result, the value calculated for x" would be in- correct, because it would be based on one of the many ratios found on line 3, and the ratios along line 3 vary. In their effort to save time, or to produce a practical number of tests economically, previous methods have erred by relying on a single point