UNIFIED DESCRIPTION OF THE NON-SINGLET SPIN-DEPENDENT STRUCTURE-FUNCTION G(1) INCORPORATING ALTARELLI-PARISI EVOLUTION AND THE DOUBLE LOGARITHMIC LN(2)(1 X) EFFECTS AT LOW-X/

A unified equation for the non-singlet spin dependent structure functi on g(1)(ns)(x,Q(2))=g(1)(p)(x,Q(2))-g(1)(n)(x,Q(2)) which incorporates the complete leading order Altarelli-Parisi evolution at finite x and double logarithmic ln(2)(1/x) effects at x-->0 is formulated. This eq uation is solved assuming simple phenomenological parametrisation of t he non-perturbative part of the structure function. Reasonable agreeme nt is obtained with the recent data obtained by the Spin Muon Collabor ation. Predictions for the small x behaviour of g(1)(ns)(x,Q(2)) in th e kinematical range which may be relevant for the possible HERA measur ements are given. The contribution to the Bjorken sum coming from the region of very small values of x is quantified. Extrapolation of g(1)( x,Q(2)) to the region of small x and small Q(2) is also discussed. (C) 1998 Elsevier Science B.V.