The thesis is concerned with the relation between a microscopic approach and a macroscopic approach to the study of the nuclear binding energy as a function of neutron number, proton number and nuclear deformations. First of all we give a general discussion of the potential energy of a system which can be divided into a bulk region and a thin skin layer. We find that this energy can be written down in the usual liquid drop type of expression, i.e., in terms of the volume, the surface area and other macroscopic properties of the system. The discussion is illustrated by a study of noninteracting particles in an orthorhombic potential well with zero potential inside and infinite potential outside. The total energy is calculated both exactly (a microscopic approach) and also from a liquid drop type of expression (a macroscopic approach). It turns out that the latter approach reproduces the smooth average of the exact results very well. We next make a digression to study the saddle point shapes of a charged conducting drop on a pure liquid drop model. We compare the properties of a conducting drop with those of a drop whose charges are distributed uniformly throughout its volume. …