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Expressions for the P,T-violating NN potentials are derived for $\pi$, $\rho$and $\omega$ exchange. The nuclear matrix elements for $\rho$ and $\omega$exchange are shown to be greatly suppressed, so that, under the assumption ofcomparable coupling constants, $\pi$ exchange would dominate by two orders ofmagnitude. The ratio of P,T-violating to P-violating matrix elements is foundto remain approximately constant across the nuclear mass table, thusestablishing the proportionality between time-reversal-violation andparity-violation matrix elements. The calculated values of this ratio suggest aneed to obtain an accuracy of order $ 5 \times 10^{-4}$ for the ratio of thePT-violating to P-violating asymmetries in neutron transmission experiments inorder to improve on the present limits on the isovector pion coupling constant.Comment: 17 pages, LaTeX, no figure

P,T-violating nuclear matrix elements in the one-meson exchange approximation