In this paper we report the first results on a medium survey program conducted in the 2-10 keV energy band using data from the GIS2 instrument onboard the ASCA satellite .

We have selected from the ASCA public archive ( as of February 14 , 1996 ) 87 images which are suitable for this project .
Sixty serendipitous X-ray sources , with a signal-to-noise ratio greater than 3.5 , were found .
The 2-10 keV flux of the detected sources ranges from \sim 1.1 \times 10 ^ { -13 } ergs cm ^ { -2 } s ^ { -1 } to \sim 4.1 \times 10 ^ { -12 } ergs cm ^ { -2 } s ^ { -1 } .

Using this sample we have extended the description of the 2-10 keV LogN ( > S ) –LogS to a flux limit of \sim 6.3 \times 10 ^ { -14 } ergs cm ^ { -2 } s ^ { -1 } ( the faintest detectable flux ) , i.e .
about 2.7 orders of magnitude fainter than the Piccinotti et al .
( 1982 ) determination .
The derived number-flux relationship is well described by a power law model , N ( > S ) = K \times S ^ { - \alpha } , with best fit values \alpha = 1.67 \pm 0.18 and K = 2.85 \times 10 ^ { -21 } deg ^ { -2 } .

At the flux limit of the survey about 27 % of the Cosmic X-ray Background in the 2-10 keV energy band is resolved in discrete sources .
A flattening of the number-flux relationship , within a factor of 10 from the flux limit of the present survey , is expected in order to avoid saturation .

The implications of these results on the models for the origin of the hard X-ray background are briefly discussed .