HARMO]SriC A:srALYSIS AND PREDICTION OF TIDES. 



173 



Table 2. — Astronomical quantities and relations. 

 [Derived from Table 1.] 



Epoch 

 (Gregorian calendar, Greenwich mean civil time). 



1800, Jan. 1, hour 

 1900, Jan. 1, hour 

 2000, Jan. 1, horn- 



Mean longitude of lunar and solar elements. 



Moon. 



342. 313 

 277. 026 

 211. 744 



Lunar 



perigee. 



V 



225.453 



334. 384 



83.294 



Sun. 

 ft 



280.407 

 280. 190 

 279. 973 



Solar 



perigee. 



Pi 



279. 502 

 281. 221 

 282. 940 



Moon's 

 node. 



N 



33.248 

 259. 156 

 125.069 



Rate of change in mean longitude (epoch, Jan. 1, 1900). 



Per 



Julian century 



(36525 days). 



Per 



common year 



(365 days). 



Per 

 solar day. 



Per 

 solar hour. 



Moon 



lunar perigee . 

 Sun 



Solar perigee . , 

 Moon's node.. 



1336 r.+307. 892 



11 r.+109.032 



100 )•.+ 0. 769 



1.719 



-(5r.+134.142) 



13 r.+ 129. 384, 82 



40.662,47 



359.761,28 



0. 017, 18 



-19.328,19 



13.176,396,8 

 0.111,404,0 

 0.985,647,3 

 0.000,047,1 

 -0.052,953,9 



.7=0.549,016,53 



W=0.004,641,83 



7,=0. 041,068,64 



©1=0.000,001,96 



-0.002,206,41 



Note.— r=l revolution or 360°. 



Inclination of earth's equator to the ecliptic (u>), epoch Jan. 1, 1900 =23.452 



IncUnation of moon's orbit to the ecliptic (i) = 5. 145 



Eccentricity of earth's orbit (ft), epoch Jan. 1, 1900 — 0. 01675 



Eccentricity of moon's orbit (e) =0. 05490 



Mean radius of earth (o) =3,958.89 statute miles= 20,902,900 feet 



Mass of moon (Jlf) / mean radius of earth (o) \3 „„„„„„„„,,„„„ 



AT r ixt-tt^XI 3V-T ; -T-^ I =0.000,000,055,900 



Mass of earth (jB)Vmean distance of moon (c)/ """")""">" ^j^"" 



Mass of sun (g) / mean radius of earth (a) V ^0.000,000.025,806 

 Mass of earth (£)^\mean distance of sun (ci)/ ' ' ' 



Mass of sun (g) / mean distance of moon (c) \» » ./.■■/., ^ 

 Mass of moon ( jlf) \ mean distance of sun (ci) / ~ " ~ 



x( J Y=0.000,000,000,926,51; -gx( ^y=0.000,000,000,001,10 



rate of change in longitude of sum (i;) .,^ »_. o^. 

 rate of change in longitude of moon (,a)~ ' ' ^"^ 



e2i=0.000281 £2=0.003014 7n29= 0.005,596 7n«=0.004,107 



slQ &)=0.39798 

 cos 01=0.91739 



sin2 £0=0.15839 sin J<o= 0.20323 sin^ Jaj= 0.04130 

 C0S2 c»=0.84161 cos !&)= 0.97913 COS^ |u=0.95870 



sin 1=0.08968 sin*z= 0.00804 sin 2a>= 0.73021 sinno)= 0.001 71 

 COS 1=0.99597 cos2?= 0.99196 cos 2a)=0.68322 COS« |a)= 0.91910 



fVU W v; .. Is^vvWw-- *iW-^ ^ ^ f ^ ^ ^ i^i^'V:) 



U 



