The hyper-Rayleigh scattering technique has been applied to suspensions of purple membranes, and the size distribution of these membranes, deposited on a mica surface, has been determined by means of atomic force microscopy. A model is developed to express the first hyperpolarizability of a purple membrane fragment in terms of the first hyperpolarizability of the protein bacteriorhodopsin and the angle of the retinal protonated Schiff base with the surface of the membrane. By measuring the depolarization ratio of the scattered second-harmonic light, we deduce a value of (10 degrees +/- 1 degrees) for the magnitude of this angle. The arrangement of the proteins in the membrane is found to be predominantly octopolar. Using this angle and the average size of the purple membrane fragments, we find a value of (2000 +/- 400) x 10(-30) esu for the hyperpolarizability of the protein if we assume that the proteins in a purple membrane patch can be treated as correlated scatterers. Alternatively, using a value of 2100 x 10(-30) esu for the hyperpolarizability of the protein, we calculate the average number of proteins in a purple membrane patch (2530). This average is in good agreement with the median (2270) and the average (3470) of the size distribution of the membranes.