9 



Substituting the expression for R^jD^ previously foimd, but drop- 

 ping the squares and higher powers of i^: 



fh=MiJL sin e(l-{-3p cos 6-1) /R^ 



=SMn(r/R^) sin 6 cos ^=3/2 MfjL{r/R^) sin 29. (6) 



The terms containing "the fourth power of the moon's parallax" 

 being omitted. 



17. When P is at the surface of the earth, r becomes a, the earth's 

 radius. The line CP is evidently the vertical at P. Therefore the 

 vertical component of the lunar tide-producing force is: 



fr=^Mfi(a/R^) (3 cos^ 9-1) (7) 



and the horizontal component, in the direction of the moon, is: 



/A =3/2 MiiialR^) sin 26. (8) 



Since the vertical line CP is directed toward the zenith of the place 

 P, it is also clear that the angle 6 is the zenith distance of the moon, 

 or the complement of the moon's altitude above the horizon, 



18. Characteristics of the lunar tide-producing force. — It is evident 

 from equation (7) that the vertical component of the tide-producing 



Moon 



FiGUKE 2.— Directions of tide-producing force. 



force is a maximum when ^=0 and 180° and is then 2MiJ.alR^. It 

 is zero when cos 6=^j'ljz^, i. e., when 6 is 54°44', 125°16', 234°44', 

 and 305°16'. It reaches a maximum negative value of —Alfia/R^ 

 when ^ = 90° and 270°. Similarly the horizontal component increases 

 from zero, when 6=0, to a maximum of 3/2 M^a/R^ when ^=45°, and 

 then decreases to zero when ^=--90°, repeating this variation with 

 appropriate changes in sign in each quadrant. The resultants of 

 the horizontal and vertical components of the tide producing force, 

 for various values of 6, are shown graphically in figure 2. 



The attraction of the moon tends to pull the water of the oceans 

 toward it on the side of the earth nearest the moon, and to pull the 



