  The cluster of galaxies A2319 was observed in 1999 for 160 ks by the PCA and
HEXTE instruments aboard the RXTE satellite. No noticeable variability is seen
in the emission measured by either instrument over the 8 week observation.
Fitting the RXTE data by a single thermal component we obtain $kT = 8.6 \pm
0.1$ (90% confidence limits), a low iron abundance $Z_{F_e} \sim 0.16 \pm
0.02$, and large positive residuals below 6 keV and between 15 to 30 keV. The
quality of the fit is drastically improved if a second component is added. A
two-temperature model yields $kT_{1} \simeq 10.1 \pm 0.6$, $kT_{2}\simeq 2.8
\pm 0.6$, and of $Z_{F_e} \sim 0.23 \pm 0.03$. An equally good fit is obtained
by a combination of a primary thermal and a secondary nonthermal component,
with $kT \simeq 8.9 \pm 0.6$, and power-law index $\alpha \simeq 2.4 \pm 0.3$.
We have repeated the analysis by performing joint fits to both these RXTE
measurements and archival ASCA data. At most 25% of the RXTE secondary
component could be present in the ASCA data. Allowing for this difference, very
similar results were obtained, with only somewhat different values for the
temperature and power-law index in the latter model. The deduced value of
$\alpha$ is consistent with the measured spectrum of extended radio emission.
Identifying the power-law emission as Compton scattering of the radio-emitting
electrons by the CMB, we obtain $B \sim0.1-0.3$ $\mu G$ for the volume-averaged
magnetic field, and $\sim 4 \times 10^{-14}(R/2 Mpc)^{-3}$ erg cm$^{-3}$ for
the mean energy density of the emitting electrons in the central region (radius
R) of A2319.
