Hair Breakage 258 It is worth spending a moment to highlight implications arising from the presence of an exponential relationship. We are most- familiar (and therefore comfortable) with linear relationships, where a given change produces a consistent proportional response. However, in exponential relationships, a given change may yield slight alterations in one instance, and dramatic ones in others. This occurrence can be illustrated by considering the effect of fiber dimensions on the tendency for breakage. It should be remembered that stress depends not only on the magnitude of the repeating force, but also on the dimensions of the hair fibers. Therefore, a constant force applied to fibers of decreasing diameter will yield higher stresses and subsequently result in an exponentially higher tendency for breakage. By means of illustration, Figure 4 shows predictions for cycles-to-fail under a repeating 40 g load as a function of fiber diameter which arise from the same regression at 60% RH. Figure 3. Average cycles-to-fail as a function of repeating stress for Caucasian hair at 60% RH