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Studies of weak gravitational lensing by large-scale structures require themeasurement of the distortions introduced to the shapes of distant galaxies atthe few percent level by anisotropic light deflection along the line of sight.To detect this signal on 1-10 arcmin scales in a particular field, accuratemeasurements of the correlations between the shapes of order 1000-10000galaxies are required. This large-scale averaging is required to accommodatethe unknown intrinsic shapes of the background galaxies, even with carefulremoval of systematic effects. Here an alternative is discussed. If it ispossible to measure accurately the detailed dynamical structure of thebackground galaxies, in particular rotating disks, then it should be possibleto measure directly the cosmic shear distortion, as it generally leads to anon-self-consistent rotation curve. Narrow spectral lines and excellenttwo-dimensional spatial resolution are required. The ideal lines and telescopeare CO rotational transitions and the Atacama Large Millimeter Array (ALMA)respectively.Comment: 12 pages, 4 figures, Expected to appear in ApJ Letters Vol. 570, 10  May 2002. Replaced with final proof version correcting minor typo

Detecting Gravitational Lensing Cosmic Shear from Samples of Several Galaxies Using Two-dimensional Spectral Imaging