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Lecture Notes on Quantitative Analysis (Hill). New York: Putnam's Sons. Pp. 64. Price, 75 cents.
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Does the Earth rotate at a uniform rate?—In the September number of Silliman's Journal, we find a remarkable paper by Prof. Newcomb, of the Naval Observatory, Washington, to the conclusions of which we wish to call the attention of our readers.
Prof. Newcomb, who has for some time been engaged on the most difficult problem of celestial mechanics—the "Theory of the Moon's Motion"—published, in 1870, a paper referring to some of the difficulties in this theory. He has treated the lunar theory in quite an original and exhaustive manner, and, in the course of his investigations, arrived at the fact that there were certain outstanding differences between theory and observation which had not yet been accounted for by the gravitation of the known bodies of the solar system. Prof. Newcomb suggested that there were only three possible explanations of the discrepancy: 1. The mathematical analysis was not sufficiently extended; 2. The motion of the moon was affected by some force different from gravitation; 3. The time of the earth's rotation on its axis was not constant.
The second hypothesis Prof. Newcomb showed was not at all probable, since the effects of a force other than gravitation would produce variations of a different kind from the ones actually noticed: the first hypothesis Prof. Newcomb has, since 1870, been engaged in testing, and his researches have convinced him that analysis has taken cognizance of every important inequality in the moon's motion. This makes it necessary to examine rigorously the third hypothesis, viz., that the earth's time of rotation on its axis is not strictly uniform.
This explanation is, at first sight, somewhat startling, since the absolute uniformity of the sidereal day has long been supposed certain. Prof. Newcomb's researches in 1870 led him, however, to the conclusion that the earth had been rotating somewhat slower than the average rate for ten or twenty years previous to 1860; that about 1860 the rotation was accelerated, so that there was a gain of at least a second per annum till about 1872.
This hypothesis would, we must re-