EVALUATION OF ORAL ODOR 289 stimulant is known or, in relative units if the amount of the stimulant or mixture of stimulants is unknown. For purposes of this paper, the form of the relationship of g to Fair and Wells osmoscope readings is sufficient for the discussion. It can be seen in Fig. 2 that very slight changes in the I I I I I I I I0 20 30 40 50 60 70 Excitation Stimulus (Odor) g Figure 2.--Response Character- istics of the Fair and Wells Osmo- scope showing the relationship between the osmoscope settings and the intensity of the external excitation stimulus. II- 0 i i I I I I I I I I I I I i I I I 2 4 6 8 I0 12 14 16 18 Excitation Stimulus g Figure &--Graphic display of the Weber-Fechner law showing the log- arithmic relationship between the excita- tion stimulus and the minimum percepti- ble difference in sensation. From Howell (2). lationship, first reported by Weber amount of g for low values of g will cause a large change in the osmoscope readings in the range of settings of 1 through 3. As g increases, its effect upon the change in osmoscope read- ings is less although the osmoscope is very sensitive to small amounts of stimulant. A problem arises in the case of odors of high intensity: A reading of 6 on the osmoscope may be just slightly above 6 or much greater. The length of the osmoscope could be extended to make more settings pos- sible. The device will now become unwieldy, but if it can be used for clin- ical testing it might be a good com- promise. Alternately the hole sizes could be changed to alter the value of x. Since the output from the Fair and Wells osmoscope is coupled into a nonlinear detector (the human nose), the sensitivity of the detector must, nevertheless, be analyzed be- fore it can be determined whether either of the approaches will be helpful. The human nose responds to an excitation stimulus in a rela- tionship in which the subjective sensation varies as the log of the applied stimulus intensity. This re- and later elaborated by Fechner, is known as the Weber-Fechner law of sensation (2). general relationship it may be broken into several forms. forms are of interest in the study of the osmoscope. These are: h o: Ag, g where h = intensity of the sensation (subjective) and Stated in a Two of' these [2]

290 JOURNAL OF THE SOCIETY OF COSMETIC CHEMISTS g = external signal strength, and for a differential sensation, hx - h• = log g-•, [3] g• where subscripts denote a particular response to particular intensity of a given stimulant. Figure 3 shows graphic representation of the equations [2] and [3]. The greatest change in sensation results from the smallest change in the excitation when g is smallest. As g increases, the change in sensation becomes smaller. Both the detector and the osmoscope are most sensitive when the value of g is small--both become less sensitive as g increases. Therefore, the sensitivity is not increased much by increasing the number of settings on the osmoscope to record higher values of g. For this same reason, one will not gain much by increasing the value of n. What about an increase in the value of x ? By assuming a given value of g and increasing it, the difference between h for the initial value of g, and h for the new value of g will become less and less as the value of g becomes larger (equation 3). This means that an increase in x reduces the ability of the detector to sense changes in g, which now becomes larger at a greater rate. If one constructs an osmoscope in which x or n is increased, a further phenomenon will become apparent. Odors which were detectable only at settings of 4 and $ now all register as 6. That is, odors which were pre- viously reported as weaker odors seem to become stronger when it is known by the design of the instrument that the odor-producing mixture is even more dilute than before. The reason for this, which follows from an ex- tension of the Weber-Fechner law, involves the second derivative of the excitation signal strength. For purposes of this presentation, it will be stated simply without explanation. The rate of change of the change of intensity of g is proportional to the sensation h. By increasing the mixing hole size in the osmoscope, the abruptness of the presentation of the odor is increased, thereby allowing the nose to sense smaller amounts of the odor. Since we cannot alter the output characteristics of the osmoscope and detector complex, we must reduce g before we present it to the osmoscope. Simply stated the odor-containing gas must be diluted with air before intro- ducing it into the osmoscope. At a very low value of g, the changes of rate of presentation of g become small. Thus, if we make a series dilution of the oral odor gas with air before the mix enters the osmoscope, we are able to cancel the second derivative of g by recording the dilution for each individual tested at which his osmoscope reading becomes 1. In practice, this is not feasible because