1. The theory of electromagnetic wave propagation along an infinite helical conductor using (a) the Sheath Helix model and (b) the Tape Helix model has been applied to the helical aerial a result the following predictions have been made for she first time, for any pitch angle . (i) the upper frequency limit of the Endfire Helical Aerial by means of the Sheath Helix Model (ii) the upper and lower frequency limits of the Endfire Helical Aerial by means of the 'ape Helix Model. (iii) the upper and lower frequency limits of the Broadside Helical Aerial with Coaxial Conducting Cylinder using the Sheath Helix model. 2. As a result of the above theoretical investigations it has been predicted and confined experimentally that the upper frequency limit of the helical aerial is not independent of length as had previously been reported. she form of this variation can be computed and the theoretical values agree with experiment to an accuracy or better than 10%. 3. The prediction has been further made and confirmed that what was previously believed to be a lower limit of pitch angle of 5° for the Endfire Helical Aerial does not in fact exist. Satisfactory experiments have been carried out with pitch angles as lo',: as 1.8 °, which was the lowest physically possible at the frequency of operation used. It is believed now that there is no lower limit of pitch angle. 4. It has been predicted and confirmed that the free space circumferential length C equal to unity is not the centre frequency of operation of the helical aerial in general. It is the centre frequency only for short aerials using a medium helical pitch angle. for low pitch angle helices Cλ equal to unity is well above the upper frequency limit of the aerial, and for long helices this may also be the case even for a medium pitch angle. 5. It has been found that it is not always possible to neglect the effect of the ground screen on the radiation pattern of the helix. Specifically when the ground screen is (a) several wavelengths in diameter or (b) constructed of n radial wires the pattern is profoundly affected, adversely. Experiment has been limited to n≤8. 6. A Tchebycheff type of current distribution has been proposed for the helical aerial. It has beer shown theoretically, using the assumption of a constant amplitude travelling wave, that the prospect of increased directivity from this distribution is severely restricted because of the linking up turns necessary. Reduced side-lobe level has been obtained however, in agreement with the above simplified theory, over the small frequency range determined by the narrow pitch turns. The measured current distribution shows large fluctuations by comparison with the simple uniform helix. 7. General theoretical solutions which in principle enable the base velocity to be calculated, and hence the frequency limits of the aerial to be predicted, have been obtained for the first time for each of the following cases: - (i) The Sheath and Tape Helix with a Coaxial Conducting Cylinder (ii) The Tape Helix wound on a dielectric tube (iii) The Sheath Helix embedded in a dielectric medium, with a hollow coaxial tube. (iv) Two Coaxial Sheath Helices. Calculations have been carried out only in Case (i) for the Sheath Helix and approximate calculation for the Tape Helix. 8. What is believed to be a new type of helical aerial - he linearly polarised Conora--Round Helix is proposed. Some measurements have been made, and the travelling-wave analysis for the simple helix has been extended to include this case. 9. A critical review has been made of the theory that all End-Fire Travelling Wave aerials intrinsically possess the same pattern bandwidth.