538 Brown — Effects of Magnetic and Gravitational 



The libration along the lunar equator of that principal axis 

 of the moon which is directed towards the earth would have, 

 according to theory, a period of between two and three years : 

 the value is doubtful. The period of the second libration is 

 very nearly equal to a month. On examination it is seen that 

 neither of these can cause any sensible effect unless it had an 

 amplitude which would have been detected by observation. 



The third libration has a period of between 200 and 300 

 years. The time is suggestive but its direction of motion is 

 perpendicular to the moon's equator. In order to affect the 

 motion of the moon's center sufficiently it would have to give 

 rise to a libration within the moon's equator. The theory of 

 the motion of the moon about its center of mass must be 

 worked out to a higher degree of accuracy than yet obtained 

 in order to find out whether there may be a long-period term 

 of the kind and size required. On the observational side 

 sufficient material has not yet been accumulated to test the 

 existence of terms of very long period. 



An angular change of 100" in the position of any axis of 

 the moon is the smallest amount which can be detected by a 

 single observation, with the methods hitherto used. The 

 recent work of Mr. F. T. M. Stratton* shows clearly how 

 doubtful the constants of the moon's physical constitution are. 

 This is to be expected, since the librational coefficients from 

 which these constants are determined are of the orderof 100". 

 Hence a long-period vibration of 50 " is not at present excluded 

 either by theory or observation. 



10. A well known difficulty in the theory of the rotation of 

 the moon is the fact that the ellipticities, as determined from 

 observation, are some sixteen times as great as the ellipticities 

 obtained on the assumption that the outer form of the moon is 

 a level surface. It has already been mentioned that a magnetic 

 attraction between the earth and the moon would produce the 

 largest relative effect on the rotation of the moon. It may be 

 suggested that the forced vibrations which are observed have 

 their origin mainly in a magnetic attraction rather than in the 

 gravitational attraction hitherto considered. The general effect 

 is quite similar. 



Nevertheless the free librations in any case depend on the 

 ellipticities alone. If we calculate the free libration in the 

 equatorial plane with the theoretical ellipticities first men- 

 tioned, the period, instead of two or three years, becomes 14 

 years, and this may be still further increased by non-rigidity. 



A free period of 17 to 20 years is effective in producing 

 inequalities with long periods and large coefficients in the 



* Memoirs Eoy. Astron. Soc, vol. lix, pt. iv. 



