[en] The construction of an apparatus designed to detect stable fractional charges on matter, if they exist, to the level of 10^-24 per nucleon is reported and discussed. The charges on a stream of highly consistent droplets produced by the apparatus are determined by accurate measurement of the deflection of the droplets in falling through a static electric field. Maintenance of certain parameters of operation calculated to limit the random effects of electrical and aerodynamical disturbances on the droplets indicate a precision in the measurement of the charge on a droplet of 0.02e can be attained. 7 figures