59 



+ 23/16 m^ cos (2T+47i-4s+2^-2j/)] ^2 



+ cos2 X sin^ / [(1/4 + 3/8 e') cos (2r+2A,-2j;) [K2] 



+3/8 e cos {2T+2h-s-\-p-2v)] [L2] 



+sin 2X sin 7 cos^ %I [(1/2-5/4 e^) cos (r+/i,-2s+2^-i.+90°) d 



+7/4 e cos (r+/^-3s+2>+2^-v+90°) Qi 



+ 1/4 e cos (T+/i-s-:P+2^-v-90°) [Mi] 



+ 17/4 e^ cos (r+/i-4s+2^+2|-j'+90°) 2Q 



+ 105/32 me cos (7+3/^— 3s-p+2^-j/+90°)] pi 



+ sin 2X sin 7 sin^ jil (1/2-5/4 e^) cos {T+h+2s-2^-v-90°) 00 



+ sin 2X sin 27 [(1/4 + 3/8 e^) cos (r+/i-z/-90°) [Ki] 



+ 3/8ecos (T+/^+s-2?-i'-90°) Ji 



+3/8 e cos {Ti-h-s+p-u-90°)] [Mj] 



+ (1/2-3/2 sin^ X) sin^ 7(1/2-5/4 e') cos (2s-2^) Mf 



+ (1/2-3/2 sin2 X) (1-3/2 sin^ 7) [e cos (s-p) Mm 



+m' cos (2s-2/i)]}. [Msf] 



(68) 



110. Solar equilibrium tide. — The corresponding equation for the 

 solar equihbrium tide may be written at once from equation (68) by 

 substituting: 



S, the mass of the sun, for M the mass of the moon. 



Ci, the mean distance of the sun, for c. 



ei, the eccentricity of the sun's orbit, for e. 



CO (omega), the obliquity of the ecHptic, for 7. 



Pi, the longitude of the sun's perigee, for p. 



The angle s, the mean longitude of the moon, becomes identical 

 with h, the mean longitude of the sun. The angles ^ and v, the longi- 

 tude and right ascension of the intersection, become zero, as does m, 

 the relative motion of the moon and the sun; and ei is so small that a 

 number of terms dependent upon this constant may be dropped. 

 The equation of the sohir equihbrium tide then becomes: 



7/=3/2 {Sa'/Ec{')a{cos' X cos^ %c^ [(1/2-5/4 e^') cos 2T S2 



+ 7/4 61 cos {2T-h+py) T2 



+ 1/4 ei cos {2T+h-p, + lS0°)] R2 



+ cos^ X sin- CO (1/4 + 3/8 e,^) cos {2T+2h) [Ko] 



+ sin 2X sin cos^ Kco(l/2-5/4 e^^) cos (7^-/^ + 90°) Pi 



+ sin 2X sin 2co(l/4 + 3/8 e,^) cos (r+A-90°) [KJ 



+ (1/2-3/2 sin- X) sin- co(l/2-5/4 O cos 2h]. Ssa 



(69) 



111. Tide depending on fourth power of moort's parallax. — This may 

 be derived by substituting in the second term of equation (20) an 



192750 — 40- 



