The weak gravitational lensing effect, small coherent distortions of galaxy images by means of a gravitational tidal field, can be used to study the relation between the matter and galaxy distribution. In this context, weak lensing has so far only been used for considering a second-order correlation function that relates the matter density and galaxy number density as a function of separation. We implement two new, third-order correlation functions that have recently been suggested in the literature, and apply them to the Red-Sequence Cluster Survey. We demonstrate that it is possible, even with already existing data, to make significant measurements of third-order lensing correlations. We develop an optimised computer code for the correlation functions. To test its reliability a set of tests are performed. The correlation functions are transformed to aperture statistics, which allow easy tests for remaining systematics in the data. In order to further verify the robustness of our measurement, the signal is shown to vanish when randomising the source ellipticities. Finally, the lensing signal is compared to crude predictions based on the halo-model. On angular scales between roughly 1 arcmin and 11 arcmin a significant third-order correlation between two lens positions and one source ellipticity is found. We discuss this correlation function as a novel tool to study the average matter environment of pairs of galaxies. Correlating two source ellipticities and one lens position yields a less significant but nevertheless detectable signal on a scale of 4 arcmin. Both signals lie roughly within the range expected by theory which supports their cosmological origin.[ABRIDGED]
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