$ 287] Lunar Theory 369 



New methods of dealing with lunar theory were devised 

 by the late Professor John Couch Adams of Cambridge 

 (1819-1892), and similar methods have been developed by 

 Dr. G. \V. Hill of Washington ; so far they have not been 

 worked out in detail in such a way as to be available for 

 the calculation of tables, and their interest seems to be 

 at present mathematical rather than practical; but the 

 necessary detailed work is now in progress, and these and 

 allied methods may be expected to lead to a considerable 

 diminution of the present excessive intricacy of lunar 

 theory. 



287. One special point in lunar theory may be worth 

 mentioning. The secular acceleration of the moon's mean 

 motion which had perplexed astronomers since its first 

 discovery by Halley (chapter x., 201) had, as we have 

 seen (chapter XL, 240), received an explanation in 1787 

 at the hands of Laplace. Adams, on going through the 

 calculation, found that some quantities omitted by Laplace 

 as unimportant had in reality a very sensible effect on the 

 result, so that a certain quantity expressing the rate of 

 increase of the moon's motion came out to be between 

 5" and 6'', instead of being about 10", as Laplace had found 

 and as observation required. The correction was disputed 

 at first by several of the leading experts, but was confirmed 

 independently by Delaunay and is now accepted. The 

 moon appears in consequence to have a certain very minute 

 increase in speed for which the theory of gravitation affords 

 no explanation. An ingenious though by no means certain 

 explanation was suggested by Delaunay in 1865. It had 

 been noticed by Kant that tidal friction that is, the friction 

 set up between the solid earth and the ocean as the result 

 of the tidal motion of the latter would have the effect of 

 Checking to some extent the rotation of the earth ; but as 

 ^he effect seemed to be excessively minute and incapable 

 of precise calculation it was generally ignored. An attempt 

 to calculate its amount was, however, made in 1853 by 

 IVilliam Ferret, who also pointed out that, as the period 

 of the earth's rotation the day is our fundamental unit 

 of time, a reduction of the earth's rate of rotation involves 

 the lengthening of our unit of time, and consequently pro- 

 duces an apparent increase of speed in all other motions 



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