57 



k, the correction to be added to the mean longitude of the 



moon to give its true longitude. 

 h, the arc USi, the mean longitude of the sun. 

 p, the mean longitude of lunar perigee, the arc measured from 



Ui to the position of lunar perigee, if the latter moved at its 



mean rate. 

 ^ (xi), the arc UJ, the longitude, in the moon's orbit, of the 



Intersection. 

 V (nu), the arc UI, the right ascension of the Intersection. 

 6 = 0.05490, the eccentricity of the moon's orbit. 

 m = 0.074804, the ratio of the mean motion of the sun to that 



of the moon. 

 R, the true distance from the center of the earth to the center 



of the moon at a given moment. 

 c= 238,857 statute miles, the mean distance, earth to moon. 

 a=3,958.89 statute miles, the mean radius of the earth. 



The values of e and m given are those for January 1, 1900, but 

 they change but little mth the time. 



106. The height of the lunar equilibrium tide is, from equation (16): 



u=y2{Ma'/ER')a{3 cos^ ^-1) (16) 



In which M is the mass of the moon and E the mass of the earth. 

 The ratio M/E has a value of 1/81.45. 

 As shown in equation (21): 



cos 0=sin X sin 5+cos X cos 8 cos H (21) 



From the right spherical triangle IM^M: 



sin 5=sin / sin IM (60) 



From the right spherical triangle MM^Pi 



cos 5 cos H=cos PiM (61) 



And from the spherical triangle IPiM: 



cos PiM=cos IM cos 7Pi+sin IM sin IP^ cos / (62) 



From the figure: 



IM= U,M- UJ=s+k-^ (63; 



and: 



IP,= US,-\-S,Pr- UI=h+T-v (64) 



