The probability that the most accurate method of determining the solar parallax now available is that resting on the measurement of the velocity of light, has led to the acceptance of the following paper as one of the series having in view the increase of our knowledge of the celestial motions. The researches described in it, having been made at the United States Naval Academy, though at private expense, were reported to the Honorable Secretary of the Navy, and referred by him to this Office. At the suggestion of the writer, the paper was reconstructed with a fuller general discussion of the processes, and with the omission of some of the details of individual experiments.