Detailed results are reported for the connectivity properties of a system of discs of unit radius free to be situated anywhere within a square of area 2L². Ordinary lattice percolation would correspond to the discs being situated on the vertices of a square root 2L* square root 2L lattice. Computer simulations are carried out for a sequence of increasing system sizes ranging from L=20 to L=1000; for each value of L a large number of realisations are generated for 25 values of the disc concentration x. The authors calculate a variety of estimates for the threshold parameter x_c, as well as the critical exponents beta , gamma , tau , and nu . Their exponent estimates are in close agreement with accepted values for ordinary lattice percolation, therefore this continuum system appears to be in the same 'universality class' as lattice percolation.