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It is shown that in certain types of directional antenna arrays the gain can be increased by arranging so that waves going from the array elements in the direction of maximum transmission are not strictly in phase at large distances. Three examples are given, an end-fire array and two antennas designed to radiate, as far as possible, only in a horizontal plane. In the case of the end-fire array it is shown that readjustment of any existing antenna according to the ideas proposed here will increase the gain by about 1.8. The other two examples correspond to the kind of directivity generally desired in a broadcast antenna. One of these consists of short antennas placed in concentric rings. A typical array of this type containing 22 short antennas with the radius of the outer ring equal to 1.39λ has a gain of 2.31 as compared with 1.56 for a vertical half-wave antenna. The other example of a horizontally radiating array consists of a single ring of short antennas. An example of this type is calculated which has a gain of 2.0 with a total of 23 antennas placed in a circle with a radius of 1.43λ. These figures are not given as the best that can be done, but only as examples.