  We have measured the spin structure functions g2p and g2d and the virtual
photon asymmetries A2p and A2d over the kinematic range 0.02 < x < 0.8 and 0.7
< Q^2 < 20 GeV^2 by scattering 29.1 and 32.3 GeV longitudinally polarized
electrons from transversely polarized NH3 and 6LiD targets. Our measured g2
approximately follows the twist-2 Wandzura-Wilczek calculation. The twist-3
reduced matrix elements d2p and d2n are less than two standard deviations from
zero. The data are inconsistent with the Burkhardt-Cottingham sum rule if there
is no pathological behavior as x->0. The Efremov-Leader-Teryaev integral is
consistent with zero within our measured kinematic range. The absolute value of
A2 is significantly smaller than the sqrt[R(1+A1)/2] limit.
