During the nineteenth century there were several speculative attempts to show that mass and energy were proportional in various ether theories. In 1873 Nikolay Umov pointed out a relation between mass and energy for ether in the form of , where . The writings of Samuel Tolver Preston, and a 1903 paper by Olinto De Pretto, presented a mass–energy relation. Italian mathematician and math historian Umberto Bartocci observed that there were only three degrees of separation linking De Pretto to Einstein, concluding that Einstein was probably aware of De Pretto's work. Preston and De Pretto, following Le Sage, imagined that the universe was filled with an ether of tiny particles that always move at speed . Each of these particles has a kinetic energy of up to a small numerical factor. The nonrelativistic kinetic energy formula did not always include the traditional factor of , since Leibniz introduced kinetic energy without it, and the is largely conventional in prerelativistic physics. By assuming that every particle has a mass that is the sum of the masses of the ether particles, the authors concluded that all matter contains an amount of kinetic energy either given by or depending on the convention. A particle ether was usually considered unacceptably speculative science at the time, and since these authors did not formulate relativity, their reasoning is completely different from that of Einstein, who used relativity to change frames.