12 



I.RECESSION OF THE EQUINOXES AND NUTATION 



the rates of precession will be 



,, '7f(P+ „3F+2«3n ioYn,t=0 



J K(P- n,P'^2n,P") " n,f= 7t 



Jc') KiF-2n,P") " nJ^h^ 



Equating («) to ((t'), &c., we deduce 



P=l cos / (cos- /'+COS 2/')=cos I (1—^ siir T) 



P'-_ 1_ sm2^;cos2/^_ j^ ^^g j^gi^ 2/' cot 2/ 



■^ 2^3 sill / "a 



P"_ L cos / Ccos /'—cos 2/')= — ,"3 cos / sin^ P. 



4/13 



Hence the formula for precession may be written 



44 ? "^' ^—"^ cos l\( 1 -'^ sinV) <— ^ sin 21' cot 2/sin «3^ 



2.«(l+>7) G 



sin- / sin 2nd . 



4«3 J 



Similarly we would get for the nutation 



4o - ? cos / cos rist. 



2«(l+>:) C «3 



The ratio of actual lunar precession to what it would be were the moon's orbit 

 in the ecliptic, is therefore expressed by 



1— I sin- /'=0.99 (very nearly).' 



The third term of (44) indicates a slight periodical variation from the true 

 elliptic motion referred to in the next paragraph. There should be a corresponding 

 term in (45) which may be obtained by the same process, bvit they are both too 

 minute to enter into computations. 



> It is worthy of remark that the formulse of Laplaee [3100] and [3101] (Dowditch) contain no 

 such coefficient qualifying tlie mean lunar precession, though one is found in all the more popular 

 solutions; neither do they contain the term (quite minute) in 2n^t of (44), but, on the other hand, 

 contain terms in 2n.^v (corresponding to the terms in 2»,< of 25 and 2G), which, referred to in the 

 fourth par. (page 9), are generally omitted as inappreciable. 



