This grant is to suppport research to extend the method of power spectrum analysis of discrete objects from two to three dimensions, and then to apply the resulting procedure to the analysis of quasar positions. The new procedure should avoid the problem associated with equidistant sampling of a distribution (only variations on scales exceeding the Nyquist scale can be detected), and make full use of all the data available. It will also provide an alternative to the two-point correlation function as a way of looking at the data. Since the power spectrum of a distribution is the Fourier transform of the autocorrelation function, the three dimensional power spectrum should be equivalent to the evaluation of the quasar autocorrelation function. The principal data base for the project will be the new Burbidge and Hewitt (1987) catalog of quasi-stellar objects, from which subsets will be selected. The application of the new procedure should shed some light on the apparently vexing question of the scale of quasar clustering in three dimensions.
