  In the quest to develop viable designs for third-generation optical
interferometric gravitational-wave detectors (e.g. LIGO-III and EURO), one
strategy is to monitor the relative momentum or speed of the test-mass mirrors,
rather than monitoring their relative position. This paper describes and
analyzes the most straightforward design for a {\it speed meter interferometer}
that accomplishes this -- a design (due to Braginsky, Gorodetsky, Khalili and
Thorne) that is analogous to a microwave-cavity speed meter conceived by
Braginsky and Khalili. A mathematical mapping between the microwave speed meter
and the optical interferometric speed meter is developed and is used to show
(in accord with the speed being a Quantum Nondemolition [QND] observable) that
{\it in principle} the interferometric speed meter can beat the
gravitational-wave standard quantum limit (SQL) by an arbitrarily large amount,
over an arbitrarily wide range of frequencies, and can do so without the use of
squeezed vacuum or any auxiliary filter cavities at the interferometer's input
or output. However, {\it in practice}, to reach or beat the SQL, this specific
speed meter requires exorbitantly high input light power. The physical reason
for this is explored, along with other issues such as constraints on
performance due to optical dissipation. This analysis forms a foundation for
ongoing attempts to develop a more practical variant of an interferometric
speed meter and to combine the speed meter concept with other ideas to yield a
promising LIGO-III/EURO interferometer design that entails low laser power.
