A variational energy calculation for an N-particle boson system has been performed. A two-body Hamiltonian, containing the phenomenological Lennard-Jones 6-10 potential, has been assumed, and the parameters of the Lennard-Jones potential have been chosen appropriate for liquid helium II. The trial wave function was assumed to be of the Jastrow type with two parameters. The value of one of the parameters was chosen to satisfy a liquid-structure-factor consistency condition. The expectation value for the ground state energy is expressed in terms of a generalized normalization integral. To evaluate the 3-N fold integrals, the normalization integral is approximated by truncating its expansion. After performing the variation, the ground-state energy is expressed as a function of the reduced particle number density. The cluster approximations used were found insufficient to effect saturation. / M.S.