We measure the voltage-supercurrent (I'ds) characteristic of three-dimensional arrays of point contacts and find V-I: with a = 2.1 zk 0.2 at the critical coherence temperature T,. This behaviour results from the following properties of the coherence transition: i) hyperscaling of critical exponents; ii) general relations satisfied by relevant parameters, in this case the supercurrent, in phase transitions; iii) the crossover exponent is V+v; iv) the paracoherent excess conductivity has the same critical exponent y as the related X-Y model susceptibility. Previously published data on granular superconductors are compatible with this description. Experiments on superconducting thin films[l-41 and junction arrays [5, 61 have shown a typical scaling behaviour Vla of the voltage-current (V-I) characteristic at the critical temperature T,. For a two-dimensional (2D) system undergoing the Kosterlitz-Thouless (KT) [7] transition it is predicted that a(TJ = 3 and that the resistance R depends exponentially (not through a power law) on (T -Tc)-* [81.

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