Recent observations of radio echoes reflected from meteor trails have given a large amount of information about the electron densities in the trails and the physical processes occurring in the atmosphere after the passage of the meteor. In t h s paper, which is Part I of three papers dealing with the work, formulae are derived for the intensity of the radio wave scattered from a meteor trail on the assumption that the electrons are created in a long narrow column, of diameter small compared with the wavelength of the radio wave. Experimental work is described which shows that the predicted variatlon of received power with wavelength is correct for the wavelength range 4.2 m. to 8 -3 m., and accordmg to preliminary results down to 1 *4 m. The formulae can then be used to measure the electron density in the trails of meteors. Of particular interest are the measurements for meteors which are also observed visually. The results show that the density in the trail of a 5th magnitude meteor (on the limit of naked eye visibility) is approximately 2 X 1O1O electrons per cm. path. Brighter meteors (N magnitude+l) produce 10le electrons per cm. path.These results are iq very good agreement with contemporary theoretical calculations. The theory is compared with earlier calculations made by Eckersley and Pierce.