A new theory is presented to describe the segregation-induced changes in grain boundary cohesion. This approach enables the changes to be calculated readily from tabulated thermodynamic data of sublimitation enthalpies and atom sizes. The current thermodynamic theory of the change in cohesion is shown to predict the same results. A general scheme is presented which shows the degree of embrittlement or of reduction in embrittlement in any given matrix for the grain boundary segregation of some 70 solutes. In agreement with experiment the calculations show that, in a ferrous matrix, Bi, S, Sb, Se, Sn and Te will be highly embrittling, followed in order of reducing effect, by P, As, Ge, Si and Cu. In increasing order of their remedial effect on embrittlement in iron are N, B and C.