Studies of weak gravitational lensing by large-scale structures require the
measurement of the distortions introduced to the shapes of distant galaxies at
the 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, accurate
measurements of the correlations between the shapes of order 1000-10000
galaxies are required. This large-scale averaging is required to accommodate
the unknown intrinsic shapes of the background galaxies, even with careful
removal of systematic effects. Here an alternative is discussed. If it is
possible to measure accurately the detailed dynamical structure of the
background galaxies, in particular rotating disks, then it should be possible
to measure directly the cosmic shear distortion, as it generally leads to a
non-self-consistent rotation curve. Narrow spectral lines and excellent
two-dimensional spatial resolution are required. The ideal lines and telescope
are 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