With a measuring instrument for measuring sample particles moving in a cuvette, for example for measuring a zeta potential or the Brownian size the particles, with a filling device for filling and an emptying device for emptying the cuvette mounted on the ends thereof and with devices for irradiating and for monitoring the particles, it is problematical always to position the cuvette correctly or in a defined manner relative to the direction of radiation and to the monitoring device. To resolve this problem, it is proposed that the cuvette member is mounted by means of a cuvette bearing and the filling and the emptying device are fastened exclusively to the cuvette in such a way that the position of the cuvette relative to the surroundings thereof is determined and defined exclusively by the cuvette bearing.