The Spin Structure Function g2

We have measured the spin structure functions g{sub 2}{sup p} and g{sub 2}{sup d} over the kinematic range 0.02 {le} x {le} 0.8 and 0.7 {le} Q{sup 2} {le} 20 GeV{sup 2} by scattering 29.1 and 32.3 GeV longitudinally polarized electrons from transversely polarized NH{sub 3} and {sup 6}LiD targets. Our measured g{sub 2} approximately follows the twist-2 Wandzura-Wilczek calculation. The twist-3 reduced matrix elements d{sub 2}{sup p} and d{sub 2}{sup n} are less than two standard deviations from zero. The data are inconsistent with the Burkhardt-Cottingham sum rule. The Efremov-Leader-Teryaev integral is consistent with zero within our measured kinematic range.