  New loop equations for all genera in $c = \frac{1}{2}$ non-critical 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 $W_3$
algebra and are equivalent to the $W_3$ constraints derived before in the
matrix-model formulation of 2d gravity. Application of these loop equations to
construction of Hamiltonian for $c = \frac{1}{2}$ string field theory is
considered.
