Teslas transmission methods rely on creating perturbations of the earths magnetic (and therefore dielectric) fields. In the same way a pebble in a lake sends out waves, Tesla was dropping "pebbles" into the "lake" which is the earths dielectric field. Unlike water however, these perturbations once energetically established require no energy to maintain so they can travel long distances. His towers, which he wanted to build "around the globe" at certain points would "pump" the field at a certain frequency and the result would be a wave "everywhere" that could then be tapped for useful energy. Because the placement and frequency was going to be resonant with the geometry of the earth the energy in could be relatively minor compared with the energy out, as you are in a sense pushing around a "heavy weight" with a small force, but when tapping that energy you are tapping off the "momentum" of the "heavy weight" so it was about as efficient as transmission can be.

Anyway this relies on a round spherical earth. In the same way, the striking of lightning around the world gives the earth its "Schumann resonance" because all the energy from the lightning is dissipated except that which is resonant with the geometry of the earth, that resonant portion remains and bounces around. It can be calculated based on the geometry of the earth and measured to be what you would expect from that geometry, essentially proving the earth round. (there are many other proofs the earth is round too, while the flat earth proofs rely on errors of scale and other unintuitive phenomena, like the horizon "appearing" flat at ground level etc)