If massive compact halo. objects (MACHOs). are detected in ongoing sea
rches, then tau(SMC)/tau(LMC), the ratio of the optical depths toward
the Small and Large Magellanic Clouds, will be a robust indicator of t
he flattening of the Galactic dark matter halo. For a spherical halo,
tau(SMC)/tau(LMC) is about 1.45, independent of details of the shape o
f the Galactic rotation curve, the assumed mass of the Galactic disk a
nd spheroid, and the truncation distance (if any) of the dark halo. Fo
r an E6 halo (axis ratio c/a = 0.4), the ratio of optical depths is ta
u(SMC)/tau(LMC) approximately 0.95, again independent of assumptions a
bout Galactic parameters. This ratio can be measured with a precision
as good as approximately 10% depending on the typical mass of the MACH
Os. If the halo is highly flattened (e.g., E6) and closely truncated (
e.g., at twice the solar galactocentric radius), then the optical dept
h toward the LMC can be reduced by a factor of approximately 2. For th
ese extreme parameters, and the assumption of a heavy Galactic disk an
d spheroid, the upper limit of the MACHO mass range to which ongoing e
xperiments are sensitive is reduced from 0(10(6)) M. to O(10) M..