This paper shows that if a,, = A + B ( i + j ) + Cij, the solutions of Smoluchowski's coagulation equation (monodisperse case) X1(O) = 1, X z ( O l = X3(O) = . . . = 0,can be expressed as equilibrium distributions conditioned on a deterministically changing (and known) parameter. A partial converse is also given. Because the equilibrium distributions are already known, this effectively solves (1) for the given a,,. If C # 0, then there is a finite critical time t = t, when the moments of the right of (1) cease to converge. We find t, for all the given a,i.