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In this paper, we propose a distributed scheme for data gathering using a mobile data collector in wireless sensor networks (WSNs). In our scheme, a mobile data collector moves along a predefined track over the sensing field and data are forwarded to nodes whose transmission disks overlap with the trajectory of the data collector; these nodes are called relaying nodes. Data are classified into two categories: delay-sensitive data and delay-tolerant data. While delay-sensitive data are sent to the data collector directly, delay-tolerant data may be sent to a nearby relaying node, where they wait for the data collector to come and pick them up. We give a theoretical analysis to quantify the impact of data collector mobility on the lifetime of the network as compared to a WSN with a stationary data collector. Moreover, we use simulations to evaluate our scheme in practice. Simulation results show that our scheme has the potential to prolong the lifetime of the network significantly.