The Michelson-Morley experiment, performed in Cleveland in 1887, proved to be the definitive test for discarding the Fresnel aether hypothesis which had dominated physics throughout the 19th century. The experiment had been suggested to Michelson by his study of a letter of James Clerk Maxwell, and a preliminary but inconclusive trial had been made at Potsdam in 1881. It seems certain that the experiment would never have been repeated except for the urging of Kelvin and Rayleigh at the time of Kelvin's Baltimore Lectures in 1884, which Michelson and Morley attended. The conclusive null result of the Cleveland experiment was decisive in its influence on Lorentz, FitzGerald, Larmor, Poincaré, and Einstein in developing their theories of the electrodynamics of moving bodies, which culminated in the special theory of relativity. The present account contains material from extensive notes and correspondence related to the work of Michelson and Morley which the writer has assembled during the past years.