An analysis has been carried out of the center-to-limb variation of the apparent sizes of the umbra, penumbra, and whole spot. It has revealed that the umbral size decreases with height. This result is interpreted in terms of the penumbral geometrical height scale. A value of 230 km, which is larger than that of the photosphere or the umbra, explains the observed decrease. An intrinsic asymmetry in the penumbra of old sunspots has also been found, the western penumbra being slightly shorter than the rest of the penumbra. This explains why the inverse Wilson effect is present, preferentially, in the western hemisphere, as found in previous investigations. A comparison with other works is also made.