Our previous theory for calculating the scattering pattern from a single aggregate of spheres deposited on a dielectric substrate is extended to deal with a dispersion of identical aggregates onto the substrate with a random distribution of their orientations. To this end the definition of the transition matrix of an aggregate is generalized to take account of the presence of the substrate; then the transformation properties under rotation of the newly defined transition matrix are used to perform analytically the required orientational averages. When the patterns calculated with this theory are compared with the calculations for a single aggregate, it can easily be seen that the features that reveal the anisotropy of the scatterers are not canceled by the averaging procedure.