  The detection of microlensing has opened the way for the development of new
methods in galactic astronomy. This series of papers investigates what
microlensing can teach us about the structure and shape of the dark halo. In
this paper we present formulas for the microlensing rate, optical depth and
event duration distributions for a simple set of axisymmetric disk-halo models.
The halos are based on the "power--law models" which have simple velocity
distributions. Using these models, we show that there is a large uncertainty in
the predicted microlensing rate because of uncertainty in the halo parameters.
For example, models which reproduce the measured galactic observables to within
their errors still differ in microlensing rate towards the Magellanic Clouds by
more than a factor of ten. We find that while the more easily computed optical
depth correlates well with microlensing rate, the ratio of optical depth to
rate can vary by a factor of two (or greater if the disk is maximal).
Comparison of microlensing rates towards the Large and Small Magellanic Clouds
(LMC and SMC) and M31 can be used to aid determinations of the halo flattening
and rotation curve slope. For example, the ratio of microlensing rates towards
the LMC and SMC is $\sim 0.7-0.8$ for E0 halos and $\sim 1.0 - 1.2$ for E7
halos (c.f. Sackett \& Gould 1993). Once the flattening has been established,
the ratio of microlensing rates towards M31 and the LMC may help to distinguish
between models with rising, flat or falling rotation curves. Comparison of
rates along LMC and galactic bulge lines-of-sight gives useful information on
the halo core radius, although this may not be so easy to extract in practice.
Maximal disk models provide substantially smaller halo optical depths, shorter
event durations and even larger model uncertainties.
