### 4. DETERMINATION OF *H*_{0}

The range of both previous and current published values for the
expansion rate, or Hubble constant, *H*_{0}
(see Figure 1a), attest to
the difficulty of measuring this parameter accurately. Fortunately,
the past 15 years has seen a series of substantive improvements
leading toward the measurement of a more accurate value of
*H*_{0}.
Indeed, it is quite likely that the 1- uncertainty in *H*_{0} is
now approaching 10%, a significant advance over the factor-of-two
uncertainty that lingered for decades. Briefly, the significant
progress can be mainly attributed to the replacement of photographic
cameras (used in this context from the 1920's to the 1980's) by
solid-state detectors, as well as to both the development of several
completely new, and the refinement of existing, methods for measuring
extragalactic distances and *H*_{0} (e.g.,
Livio, Donahue & Panagia 1997;
Freedman 1997b).

Currently there are many empirical routes to the determination of
*H*_{0}; these fall into the following completely
independent and very
broad categories: 1) the gravitational lens time delay method, 2) the
Sunyaev-Zel'dovich method for clusters, and 3) the extragalactic
distance scale. In the latter category, there are several independent
methods for measuring distances on the largest scales (including
supernovae), but most of these methods share common, empirical
calibrations at their base. In the future, another independent
determination of *H*_{0}, from measurements of anisotropies
in the cosmic
microwave background, may also be feasible, if the physical basis for
the anisotropies can be well-established.

Each of the above methods carries its own susceptibility to systematic
errors, but the methods as listed here, have completely independent
systematics. If history in this field has taught us nothing else, it
offers the following important message: *systematic errors have
dominated, and continue to dominate, the measurement of
H*_{0}. It is
therefore vital to measure *H*_{0} using a variety of
methods, and to
test for the systematics that are affecting each of the different
kinds of techniques.

Not all of these methods have yet been tested to the same degree.
Important progress is being made on all fronts; however, some methods
are still limited by sample size and small-number statistics. For
example, method 1), the gravitational time delay method, has only two
well-studied lens systems to date: 0957+561 and PG 1115. The great
advantage of both methods 1) and 2), however, is that they measure
*H*_{0} at very large distances, independent of the need
for any local calibration.