  By calculating the linear response of packings of soft frictionless discs to
quasistatic external perturbations, we investigate the critical scaling
behavior of their elastic properties and non-affine deformations as a function
of the distance to jamming. Averaged over an ensemble of similar packings,
these systems are well described by elasticity, while in single packings we
determine a diverging length scale $\ell^*$ up to which the response of the
system is dominated by the local packing disorder. This length scale, which we
observe directly, diverges as $1/\Delta z$, where $\Delta z$ is the difference
between contact number and its isostatic value, and appears to scale
identically to the length scale which had been introduced earlier in the
interpretation of the spectrum of vibrational modes. It governs the crossover
from isostatic behavior at the small scale to continuum behavior at the large
scale; indeed we identify this length scale with the coarse graining length
needed to obtain a smooth stress field. We characterize the non-affine
displacements of the particles using the \emph{displacement angle
distribution}, a local measure for the amount of relative sliding, and analyze
the connection between local relative displacements and the elastic moduli.
