A b s t r a c t. The purpose of this note is to give the m-space of W.H.Cornish and P.R.Fowler, Coproducts of De Morgan algebras, Bull. Austral. Math. Soc. 16(1977), 1-13, associated to the free De Morgan algebra over a poset. We also compute the number of elements of the free De Morgan algebra over a chain with n elements (n natural number).