Herschel was rather unfortunate in his observations of Mars. Having obtained a rough approximation from Mars’ rotation in an interval of two days—this rough approximation being, as it chanced, only thirty-seven seconds in excess of the true period, he proceeded to take three intervals of one month each. This should have given a much better value; but, as it happened, the mean of the values he obtained was forty-six seconds too great. He then took a period of two years, and being misled by the erroneous values he had already obtained, he _missed one rotation_, getting a value two minutes too great. Thirty years ago, two German astronomers, Beer and Madler, tried the same problem, and taking a period of seven years, obtained a value which exceeds the true value by only one second. Another German, Kaiser, by combining more observations, obtained a value which is within one-fifteenth of a second of the true value. But a comparison of observations extending over 200 years has enabled me to obtain a value which I consider to lie within one-hundredth part of a second of the truth. This value for Mars’ rotation-period is 24 hours 37 minutes 22·73 seconds. Here, then, we have a result so accurate, that _at some future time_ it may serve to test the earth’s rotation-period. We have compared the rotation-rate of our test-planet with the earth’s rate during the past 200 years; and therefore, if the earth’s rate vary by more than one-hundredth of a second in the next two or three hundred years, we shall—or rather our descendants will—begin to have some notion of the change at the end of that time. But in the meantime, mankind being impatient, and not willing to leave to a distant posterity any question which can possibly be answered _now_, astronomers have looked around them for information available at once on this interesting point. The search has not been in vain. In fact, we are able to announce, with an approach to positiveness, that our great terrestrial time-piece is actually _losing time_.