Batteryless sensor nodes compute, sense, and communicate using only energy harvested from the ambient. These devices promise long maintenance free operation in hard to deploy scenarios, making them an attractive alternative to battery-powered wireless sensor networks. However, complications from frequent power failures due to unpredictable ambient energy stand in the way of robust network operation. Unlike continuously-powered systems, intermittently-powered batteryless nodes lose their time upon each reboot, along with all volatile memory, making synchronization and coordination difficult. In this paper, we consider the case where each batteryless sensor is equipped with a hourglass capacitor to estimate the elapsed time between power failures. Contrary to prior work that focused on providing a continuous notion of time for a single batteryless sensor, we consider a network of batteryless sensors and explore how to provide a network-wide, continuous, and synchronous notion of time. First, we build a mathematical model that represents the estimated time between power failures by using hourglass capacitors. This allowed us to simulate the local (and continuous) time of a single batteryless node. Second, we show through simulations the effect of hourglass capacitors and in turn the performance degradation of the state of the art synchronization protocol in wireless sensor networks in a network of batteryless devices.