  I report on the cumulative results from a program started 24 years ago
designed to measure the orbital period change of recurrent novae (RNe) across
an eruption. The goal is to use the orbital period change to measure the mass
ejected during each eruption as the key part of trying to measure whether the
RNe white dwarfs are gaining or losing mass over an entire eruption cycle, and
hence whether they can be progenitors for Type Ia supernovae. This program has
now been completed for two eclipsing RNe; CI Aquilae (CI Aql) across its
eruption in 2000 and U Scorpii (U Sco) across its eruption in 1999. For CI Aql,
I present 78 eclipse times from 1991-2009 (including four during the tail of
the 2000 eruption) plus two eclipses from 1926 and 1935. For U Sco, I present
67 eclipse times, including 46 times during quiescence from 1989-2009, plus 21
eclipse times in the tails of the 1945, 1999, and 2010 eruptions. The eclipse
times during the tails of eruptions are systematically and substantially
shifted with respect to the ephemerides from the eclipses in quiescence, with
this being caused by shifts of the center of light during the eruption. These
eclipse times are plotted on an O-C diagram and fitted to models with a steady
period change (Pdot) between eruptions (caused by, for example, conservative
mass transfer) plus an abrupt period change (DeltaP) at the time of eruption.
For CI Aql, the best fit is DeltaP=-3.7^{+9.2}_{-7.3} X 10^{-7}. For U Sco, the
best fit is DeltaP=(+43+-69) X 10^{-7} days. These period changes can directly
give a dynamical measure of the mass ejected (M_ejecta) during each eruption
with negligible sensitivity to the stellar masses and no uncertainty from
distances. For CI Aql, the one-sigma upper limit is M_ejecta < 10 X 10^{-7}$
M_sun. For U Sco, I derive M_ejecta=(43+-67) X 10^{-7} M_sun.
