Stevens' Power Law

In 1957, after dozens of experiments on direct scaling, such as magnitude estimation, appeared in the literature, S. S. Stevens proposed a new law to relate sensation magnitude to stimulus intensity:

So when plotted on log-log axes, the power law plots as a straight line with a slope of the exponent.

The exponent can be greater than one representing a positively accelerated or expansive function or it can be less than one representing a negatively accelerated or compressive function. We can compare this to Fechner's law which is compressive. There are functions, such as the perception of line length that have exponents equal to 1 showing a linear relationship between stimulus physical magnitude and perceptual magnitude.

Is Stevens' law a replacement of Fechner's Law? The answer to this question must involve questions about the assumptions underlying Fechner's Law (all jnd's are alike) and the interpretation and application of these laws.

Here are a couple of graphs showing power functions:

For fun, here is a table of exponents collected by Stevens.