40G ANNUAL OF SCIENTIFIC DISCOVERY. 



their prolate spheroid form. The last two he is inclined to attribute to im- 

 perfect or prejudiced observation, observing that " in matters of scientific 

 speculation the owner of a favorite theory is prone to take great liberties 

 with things unknown." 



ACCELERATION OF THE MOON'S MOTION. 



A curious controversy has lately arisen on the subject of the acceleration 

 of the moon's motion, which is now exciting great interest among mathe- 

 maticians and physical astronomers. Professor Adams and M. Delaunay 

 take one view of the question, MM. Plana, Pontecoulant, and Hansen, the 

 other. Mr. Airy, Mr. Main, the President of the Astronomical Society, and 

 Sir John Lubbock, support the conclusions at which Professor Adams has 

 arrived. The question in dispute is strictly mathematical; and it is a very 

 remarkable circumstance in the history of astronomy that such great names 

 should be ranged on opposite sides, seeing that the point involved is really 

 no other than whether certain analytical operations have been conducted on 

 right principles; and it is a proof, therefore, if any were wanting, of the ex- 

 traordinary complexity and difficulty of these transcendental inquiries. The 

 nature and facts of the controversy are thus stated by Professor Airy, the 

 Astronomer Royal of England, in a recent paper before the Astronomical 

 Society : 



It has been known from the time of Newton that the motions of the 

 moon are disturbed by the attraction of the sun, and that a great part of the 

 effect is of the following kind, viz., that when the moon is between the sun 

 and the earth, the sun attracts the moon away from the earth; and when the 

 earth is between the sun and the moon, the sun attracts the earth away from 

 the moon; and thus, in both cases, it tends to separate the earth and the 

 moon, or diminishes the attraction of the moon to the earth. There are 

 sometimes effects of the opposite character; but, on the whole, that just 

 described is predominant. If this dimunition were always the same in 

 amount, the periodic time of the moon passing round the earth would always 

 be the same. But it was found in the last century, by Halley and Dunthorne, 

 that the periodic time is not always the same. In order to reconcile the 

 eclipses of the moon recorded by Ptolemy with modern observations of the 

 moon, it was necessary to suppose that in every successive century the moon 

 moves a little quicker than in the preceding century, in a degree which is 

 nearly represented by supposing that at each successive lunation the moon 

 approaches nearer to the earth by one inch. The principal cause of this was 

 discovered by Laplace. First, it had been shown by him and by others that 

 the attractions of the other planets on the sun and on the earth do not alter 

 the longer axis of the orbit which the earth describes round the sun, and do 

 not alter the length of the year; but they diminish slowly but continually 

 through many thousands of years the degree of ellipticity of the earth's 

 orbit. Now, when the earth is nearest to the sun, the decrement of attraction 

 of the moon to the earth (mentioned above) is greatest; and when the earth 

 is furthest from the sun, that decrement is least. It had been supposed that 

 the fluctuations of magnitude exactly balance. But Laplace showed that 

 they do not; he showed that the increased amount of decrement (when the 

 earth is nearest the sun) overbalances the diminished amount (when the 

 earth is furthest from the sun); and, therefore, that the less eccentric is the 

 earth's orbit the less does the increased amount of decrement at one part 



