During October 1971, four cesium beam atomic clocks were flown on regularly scheduled commercial jet flights around the world twice, once eastward and once westward, to test Einstein's theory of relativity with macroscopic clocks. From the actual flight paths of each trip, the theory predicts that the flying clocks, compared with reference clocks at the U.S. Naval Observatory, should have lost 40 +/- 23 nanoseconds during the eastward trip, and should have gained 275 +/- 21 nanoseconds during the westward trip. The observed time differences are presented in the report that follows this one.