Study of Ly alpha absorption lines in the spectra of double line-of-si
ght (DLOS) quasars holds the promise of diagnosing the nature of the s
tructures that give rise to Ly alpha absorption. Based on simulations
of DLOS with various separations through a single population of absorb
ers, four tests have been designed to diagnose absorber mass distribut
ions (smoothly varying with radius or irregular), geometries (spherica
l or disk/slab-like), and kinematics (isotropic or systematic velociti
es). Applying the tests to existing data at z similar to 2 we find the
following. (1) The observed neutral hydrogen column density (N-H) dis
tributions of Ly alpha lines coincident to both LOSs are consistent wi
th a smooth mass distribution. (2) Observed large anticoincident N-H v
alues are not consistent with a single population of smooth spherical
absorbers, which should exhibit sharp cutoffs at small N-H in the N-H
distribution. (3) There is marginal evidence that the observed rms val
ue of velocity differences between coincident lines increases with DLO
S separation, as is expected for disk/slab-like absorbers that have sy
stematic velocity fields. (4) The observed velocity dispersion along a
single LOS is small compared to the rms difference between widely sep
arated LOS, which is not consistent with models of cloudlets moving is
otropically within a spherical structure. Overall, only a smooth disk/
slab-like model with systematic velocities remains consistent with the
inferred properties of a single population of Ly alpha absorbers.