The term transferral or transmission or transference line points to a specialized wire manufactured from copper or aluminum laid out with excellent dielectric or non-conductor and used for the transferral of electrical energy. Generally, a transferral line has a resistor put up by the two wires taken together, an inductor, a shunt conductance and a capacitor. The four quantities form the principal criterion of the transferral lines, and they turn on the class and assembly of transferral lines. Traditionally, the wave equations of transferral lines are examined by the Fourier transform or Laplace Transform. These transform procedures are very opportune for examining typical wave equations of electric transferral lines. The RT is the latest integral transform technique that has been tried to examine the boundary value differential equations standing up in separate engineering scopes. This paper disburses the solution of wave equations of transferral lines having negligible losses to earth or deck through dielectric by the double RT. The double RT will transpire to be a very positive tool for examining the wave equations of transferral lines.