The odd-order terms T 3±3(S) and T 5±3(S) are introduced into the C 3 h symmetry spin Hamiltonian for the Gd 3+ [ 4f 7; 8S 7 2 ] ion in lanthanum ethyl sulfate without violating time-reversal invariance by interpreting the ground-state eigenfunction as | M z >′ = α|4 f 7, 5 p 6; M z > + β|4 f 8, 5 p 5 ; M z >. The weak-magnetic-field behavior of the resulting eigenvalues is examined to determine whether their behavior is consistent with the experimental results reported recently by Shing and Buckmaster ( J. Magn. Resonance 21, 295 (1976)). It is found, in agreement with these results, that the apparent g values of the transitions differ in weak and strong magnetic fields, the g values of the |+ m>′ ↔ |+ m+1 >′ and |− m>′ ↔ |− m−1>′ transitions differ, and the extrapolated zero-field splittings of the various transitions differ from the true splittings. However, the sign of the zero-field splitting of the |+ 3 2 >′ ↔ |+ 1 2 >′ and |− 3 2 >′ ↔ | 1 2 >′ transitions is incorrect when the applied weak magnetic field is parallel to the crystal symmetry axis and a zero-field splitting of the same magnitude but opposite sign is predicted for the |+ 5 2 >′ ↔ |+ 3 2 >′ and |+− 5 2 >′ ↔ |− 3 2 >′ transitions which is not observed experimentally. Consequently it is concluded that the inclusion of these terms is unlikely to explain the anomalous zero-field splitting inferred from weak-magnetic-field variable-frequency EPR measurements.