Arrangements were made not very long ago, by which the astronomical work of Greenwich Observatory, for a long time directed almost exclusively to time observations, should include the study of the sun, stars, planets, and so forth. Amongst other work which was considered suited to the National Observatory was the application of spectroscopic analysis to determine motions of recession and approach among the celestial bodies. Some of these observations, by the way, were made, we are told, “to test the truth of Doppler’s principle,” though it seems difficult to suppose for an instant that mathematicians so skilful as the chief of the Observatory and some of his assistants could entertain any doubt on that point. Probably it was intended by the words just quoted to imply simply that some of the observations were made for the purpose of illustrating the principle of the method. We are not to suppose that on a point so simple the Greenwich observers have been in any sort of doubt. At first their results were not very satisfactory. The difficulties which had for a long time foiled Huggins, and which Secchi was never able to master, rendered the first Greenwich measures of stellar motions in the line of sight wildly inconsistent, not only with Huggins’s results, but with each other. Secchi was not slow to note this. He renewed his objections to the new method of observation, pointing and illustrating them by referring to the discrepancies among the Greenwich results. But recently a fresh series of results has been published, showing that the observers at Greenwich have succeeded in mastering some at least among the difficulties which they had before experienced. The measurements of star-motions showed now a satisfactory agreement with Huggins’s results, and their range of divergence among themselves was greatly reduced. The chief interest of the new results, however, lay in the observations made upon bodies known to be in motion in the line of sight at rates already measured. These observations, though not wanted as tests of the accuracy of the principle, were very necessary as tests of the qualities of the instruments used in applying it. It is here and thus that Secchi’s objections alone required to be met, and here and thus they have been thoroughly disposed of. Let us consider what means exist within the solar system for thus testing the new method.