Loop equations for loops with Ising spins either all up or all down in c=1/2 noncritical string theory

New loop equations for all genera in c=1/2 noncritical string theory are constructed. Our loop equations include two types of loops: loops with all Ising spins up (+ loops) and those with all spins down (- loops). The loop equations generate an algebra which is a certain extension of W3 algebra and are equivalent to the W3 constraints derived before in the matrix-model formulation of 2D gravity. The application of these loop equations to the construction of a Hamiltonian for c=1/2 string field theory is considered. copyright 1996 The American Physical Society