530 Brown — Effects of Magnetic and Gravitational 



The mathematical developments by which the statements 

 made below have been obtained are somewhat long and 

 tedious. Since the results are either of a negative character 

 or are obtained from hypotheses for which there is little or no 

 collateral evidence, it seems unnecessary to develop at length 

 the methods employed. When a disturbing function has once 

 been obtained, it has now become a simple matter to compute 

 rapidly the effect on the motion of the moon with the formulae 

 employed for the planetary terms, so that the details can be 

 given at any time when the need for them may arise. 



2. The outstanding inequalities in the moorts motion. — On 

 several occasions during the past thirty years, Newcomb has 

 examined the observations of the moon to try and find out 

 what outstanding secular or long-period inequalities there may 

 be in its motion which have not been explained by theory. Of 

 these, the best known is the slow decrease in its period which 

 increases its apparent longitude by 2" multiplied by the square 

 of the number of centuries from the epoch of reckoning. 

 This is generally ascribed with good reason to tidal friction 

 and it is not necessary to consider other causes of change except 

 for the purpose of finding the amount of the frictional effect. 



But Newcomb has also discovered a large change which 

 appears to be periodic and which he deduced from observa- 

 tions of occultations of stars by the moon. His last paper* 

 includes observations of this kind from the beginning of the 

 seventeenth, century, a range of nearly 300 years. The change 

 appears to be periodic, with a coefficient of about 12", a period 

 of about 270 years and a phase which puts its maximum effect 

 near the year 1795. Mr. P. H. Cowell makes the period about 

 350 years and the coefficient 18" on the assumption that there 

 is no secular change to be ascribed to tidal friction.f It is 

 this long-period term for which no cause has as yet been 

 assigned. There are also indications of a term with a period 

 of about 60 years and a coefficient between 2" and 3" ; also a 

 term with a period of some 20 years and a coefficient rather less 

 than V . The last may possibly disappear when a comparison 

 with the new tables of the moon's motion has been made and 

 the arbitrary constants properly adjusted. 



3. Errors due to observation or theory. — It is quite a simple 

 matter to show that the peculiarities of observations on the 

 moon cannot produce such a term. The majority of them 

 are made at night and not very near new moon, and the moon 

 itself has librations which alter its apparent diameter, but 

 none of these can give rise to so large a term. There is the 

 possibility of errors in Hansen's tables ; but with the correc- 



* Monthly Notices E. A. S., vol. lxix, p. 164. 

 f Monthly Notices E. A. S., vol. lxv, p. 84. 



