  We present a physically motivated explanation for the observed, monotonic
increase in slope, and the simultaneous (and also monotonic) decrease in the
width/scatter of the Leavitt Law (the Cepheid Period-Luminosity (PL) relation)
as one systematically moves from the blue and visual into the near and
mid-infared. We calibrate the wavelength-dependent, surface-brightness
sensitivities to temperature using the observed slopes of PL relations from the
optical through the mid-infrared, and test the calibration by comparing the
theoretical predictions with direct observations of the wavelength dependence
of the scatter in the Large Magellanic Cloud Cepheid PL relation. In doing so
we find the slope of the Period-Radius (PR) relation is c = 0.724 +/- 0.006.
Investigating the effect of differential reddening suggests that this value may
be overestimated by as much as 10%; however the same slope of the PR relation
fits the (very much unreddened) Cepheids in IC1613, albeit with lower
precision. The discussion given is general, and also applies to RR Lyrae stars,
which also show similarly increasing PL slopes and decreasing scatter with
increasing wavelength.
