The cluster of galaxies A2319 was observed in 1999 for \sim 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 \sim 8 week observation .
The quality of the data allows , for the first time , a meaningful search for emission whose spectral properties are distinct from those of the primary thermal emission with ( previously measured ) mean temperature in the range 8 - 10 keV .
Fitting the RXTE data by a single thermal component we obtain kT = 8.6 \pm 0.1 ( all errors are 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 which is consistent with previously measured values .
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 ( photon ) 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 ( kT = 9.2 \pm 0.5 ) and power-law index ( \alpha \simeq 2.5 \pm 0.3 ) in the latter model .
The deduced value of \alpha is consistent with the measured spectrum of extended radio emission in A2319 .
Identifying the power-law emission as Compton scattering of the radio-emitting electrons by the CMB , we obtain B \sim 0.1 - 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 .