function raph(gam,z1,z2,a1,a2)
c     ==============================
c
c     auxiliary function for subroutine hedif
c
      INCLUDE 'IMPLIC.FOR'
c
      b=1+gam
      c=z1+z2*gam
      d=a1+a2*gam
      e=(1+z1)+gam*(1+z2)
      den=(c*d/(gam*b))+(d*(z1-z2)**2/(b*e))
      dnum=e*(a2*z1-a1*z2)+d*(z2-z1)
      dgam=dnum/den
      raph=dgam
      return
      end