We have determined distances to 100 galactic classical Cepheids on a homogeneous system with an improved version of the surface brightness technique, using the extensive northern Cepheid observations of Moffett and Barnes, and the southern Cepheid observations of Gieren. The period-luminosity relations in the V bandpass obtained for the northern and southern Cepheid samples are found consistent, and the absolute magnitudes have been combined into a two-hemisphere PL(V) relation which isMv= -1.371 -2.986 log P. ±0.095 ±0.094 This is the currently most precise Cepheid PL(V) relation from the surface brightness technique. Typically Mv can be obtained from this relation for Cepheids with periods in the range 3 to 45 days to better than ±0.06 mag, if all the scatter in the relation is observational, or ±0.27 mag, if all the scatter is cosmic in origin. We compare our result to other recent observational determinations of the PL(V) relation and find consistency among the results produced by the surface brightness method, main-sequence fitting of open clusters and associations containing Cepheids, Hβ photometry, and statistical parallaxes. In particular, there is no significant difference between the surface brightness and ZAMS-fitting Cepheid distance scales. The agreement between the ZAMS-fitting distance scale and the fully independent surface brightness distance scale provides extremely persuasive evidence that both methods are free of significant systematic errors at the ±0.10 mag level. We show that there is no significant correlation between the residuals of the Mv from the PL(V) relation and the residuals of the intrinsic (B - V) colors of the Cepheids from the mean period-color relation, making it impossible to find a PLC relation from our data. After correcting the Cepheid distances for the small, theoretically predicted metallicity dependence of the surface brightness technique, we find no significant trend in the Mv residuals from our PL(V) relation with the galactocentric distances of the Cepheids. While the Cepheids become intrinsically bluer as their radial distances from the Galactic center increase, their mean absolute magnitudes, at a given period, do not depend on their galactocentric distances at a significant level, which is an important property in view of the use of Cepheid variables as extragalactic distance indicators.