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A practical method for calculating the effect of a four-terminal network upon a frequency-modulated wave being transmitted through it is developed and demonstrated. The form of the solution is simple enough to be applied by anyone familiar with electric circuits. No knowledge of calculus or higher mathematics is required; nor is the solution restricted in any way, being equally accurate and practical for large and small values of modulation index, and for any physical network. In order to determine whether or not a particular network problem involving a frequency-modulated input wave may be analyzed from the "instantaneous frequency" viewpoint, a test, or validity condition, has been developed. This test quickly classifies the problem either as one for which only a complete, straightforward analysis determines the response, or as one for which a quasi-steady state exists. The quasi-steady state is a condition under which the amplitude-instantaneous-input-frequency envelope and the phase-shift-instantaneous-input-frequency envelope of the output wave approach closely enough to the steady-state-amplification-frequency and phase-shift-frequency characteristics of the network.