10 



earth away from the water on the other side. The resultant tide- 

 producing forces on the side of the earth away from the moon must 

 balance the tide-producing forces on the side toward the moon, for 

 otherwise the total attraction between the earth and the moon would 

 not be the same as though the respective masses of these two bodies 

 were concentrated at their centers. Because, however, of the some- 

 what greater attraction by the moon on the nearer area of the earth, 

 the tide-producing forces on the two sides of the earth are not exactly 

 symmetrical. This variation in the tide-producing force is expressed 

 by the term containing the fourth power of the moon's parallax. 

 It tends to mould the surfaces of the ocean into a very slightly pear- 

 shaped variation from a perfect oval (fig. 8, par. 32). 



19. The solar tide-producing force.- — Designating the mass of the 

 sun by S, and its distance from the earth by Ri, and its zenith distance 

 at the point Phj di, the vertical component of the solar tide-producing 

 force at the earth's surface is evidently, from equation (7): 



fr, = Sfx {a/R,') (3 cos^ d^-l) (9) 



and the horizontal component, from equation (8) : 



Jhi = S/2SijL(a/R{') sin 2di (10) 



The maximum value of the vertical component is 2SiJ.a/Ri^. Its 

 ratio to the maximum value of the vertical lunar component is : 



{2Sfjia/R,')/i2M,xa/R') = (S/AI) (R'/R,') 



The mass of the sun, S, is 27,000,000 times the mass of the moon, 

 M; but the distance of the sun from the earth, Ri, is about 389 times 

 the distance, R, of the moon from the earth. Substituting these 

 values, the ratio of the maximum values of the solar to the lunar 

 tide-producing force becomes 27,000,000/58,863,869=0.46. Despite 

 its enormously greater mass, the tide-producing force of the sun is 

 less than half that of the moon, because of its greater distance. 



20. A consideration of figure 3 shows that when the moon is full, 

 M", or at change, M', the solar tide-producmg force w^ill tend to 

 increase the lunar tide-producing force, while when the moon is at 

 quadrature, at M' " and M" the solar tide-producing force will tend 

 to decrease the lunar tide-producing force. At the full and change 

 of the moon, therefore, liigh waters tend to be higher and low waters 

 lower, than at other phases of the moon, thus producing the spring 

 tides at full and change, and neap tides at quadrature (par. 2). 



21. Tlie tide-producing forces are minute. — The force of gravity at 

 every point on the earth's surface is Eixja-, E being the mass of the 

 earth, a its radius, and /i the gravitational attraction between two 



