Probably the most significant link between research into Earth tides and seismology is connected with the first attempts to measure the Earth's effective elasticity using these tides. In 1863 William Thomson (Lord Kelvin) published his famous paper "On the rigidity of the Earth", which describes how these observation could determine the mean rigidity of the Earth. This current paper sets out to describe some important developments in this common area of study between seismology and earth tide research until the middle of the twentieth century.