A description is given of a precise technique for measuring the threshold for acoustic cavitation inception. The system, which is automated so as to remove operator involvement, utilizes a slow ramping of the acoustic pressure amplitude until cavitation occurs. The detection criterion is the generation of a sufficiently intense sonoluminescent signal. Measurements made in filtered water show a well-defined, reproducible, and stable cavitation threshold. Measurements of the dependence of the threshold on filter size, on time, and on the concentration of dissolved ions for various salts are also presented. Many of these results appear anomalous.