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An attempt is made to explain, analytically, the observed shape of the characteristic of kinescopes, which seems to follow a simple power law with an exponent between 2 and 2.5. The difference from Langmuir-Childs law is due to the fact that the active-cathode area varies with grid voltage according to another power law. The theory is applied to the modulator section of a conventional TV picture tube and also to various structural modifications thereof. As to the emission characteristic, gamma is consistently found to lie between 2.4 and 2.5 and seems to be little affected by structural alterations. The mu factor, on the other hand, is strongly influenced by any one of the changes in the four system parameters. An experimental tube was built to check some of the predictions of the above theory. For the cathode current, a gamma value of 2.43 was observed. The useful screen current followed a power law with an exponent of 1.9. The mu factor of this tube was found to fall within two per cent of the value computed from (15) of this paper.