We present a study of the angular correlation function as measured in the William Herschel Deep Field , a high galactic latitude field which has been the subject of an extensive observing campaign from optical to infrared wavelengths .
It covers 50 arcmin ^ { 2 } and with it we are able to investigate the scaling of the angular correlation function to B \sim 28 , R,I \sim 26 , K \sim 20 and H \sim 22.5 .
We compare our measurements to results obtained from the smaller Hubble Deep Field .
To interpret our results , we use a model which correctly predicts colours , number counts and redshift distributions for the faint galaxy population .
We find that at fixed separation the amplitude of \omega ( \theta ) measured in BRI bandpasses is lower than the predictions of a model containing with no luminosity evolution and stable clustering growth in proper co-ordinates .
However , in the near-infrared bandpasses , our measurements are consistent with the predictions of an essentially non-evolving K - selected galaxy redshift distribution .
In the range B \sim 27 - 28 we find that our correlation amplitudes are independent of magnitude , which is consistent with the observed flattening of the number count slope and correspondingly slower increase of the cosmological volume element expected at these magnitudes .

If our luminosity evolution models provide a correct description of the underlying redshift distributions ( and comparisons to available observations at brighter magnitudes suggest they do ) , then our measurements in all bandpasses are consistent with a rapid growth of galaxy clustering ( 0 < \epsilon < 2 in the normal parametrisation ) on the sub-Mpc scales which our survey probes .
We demonstrate that this rapid growth of clustering is consistent with the predictions of biased models of galaxy formation , which indicate that a rapid rate of clustering growth is expected for the intrinsically faint galaxies which dominate our survey .