We have used the infrared Barnes-Evans surface brightness technique to derive the radii and distances of 34 Galactic Cepheid variables .
Radius and distance results obtained from both versions of the technique are in excellent agreement .
The radii of 28 variables are used to determine the period-radius relation .
This relation is found to have a smaller dispersion than in previous studies , and is identical to the period-radius relation found by Laney & Stobie from a completely independent method , a fact which provides persuasive evidence that the Cepheid period-radius relation is now determined at a very high confidence level .
We use the accurate infrared distances to determine period-luminosity relations in the V , I , J , H and K passbands from the Galactic sample of Cepheids .
We derive improved slopes of these relations from updated LMC Cepheid samples and adopt these slopes to obtain accurate absolute calibrations of the PL relation .
By comparing these relations to the ones defined by the LMC Cepheids , we derive strikingly consistent and precise values for the LMC distance modulus in each of the passbands which yield a mean value of \mu _ { \circ } ( LMC ) = 18.46 \pm 0.02 .

By analyzing the observed dispersions of the PL relations defined by the LMC and Galactic samples of Cepheids , we disentangle the contributions due to uncertainties in the reddenings , in distance measurement and due to metallicity effects , and we estimate the intrinsic dispersion of the PL relation with the Wesenheit function .
Assuming that the Galactic Cepheid distances are typically accurate to \pm 3 \% ( as shown in a previous Paper ) , and an intrinsic spread in [ Fe/H ] of \sim 0.4 dex among the Cepheids of our sample as obtained by Fry & Carney , the observed dispersion of the Galactic Cepheid PL relation suggests a metallicity dependence of \Delta \mu / \Delta { [ Fe / H ] } \approx 0.2 , about half the value suggested by Sasselov et al .
from EROS data .
When we apply this correction , the LMC distance modulus is increased to 18.52 \pm 0.06 with most of this uncertainty being due to the adopted metallicity correction .

Our results show that the infrared Barnes-Evans technique is very insensitive to both Cepheid metallicity and adopted reddening , and therefore a very powerful tool to derive accurate distances to nearby galaxies by a direct application of the technique to their Cepheid variables , rather than by comparing PL relations of different galaxies , which introduces much more sensitivity to metallicity and absorption corrections which are usually difficult to determine .