17 



The numerical value of S/E is 333,432; and the mean distance, Ri, 

 from the earth to the sun, is 92,897,416 statute miles. The substitu- 

 tion of these values gives : 



-^1 = 0.270(3 cos^^i-l) 



The maximum range of the solar equilibrium tide is 3X0.270=0.810 

 feet. 



32. Equilibrimn tide dependent on the fourth power of the moon's 

 parallax. — If the second term of equation (4), paragraph 15, is included 

 in the derivation of the lunar tide-producing potential, paragraph 22, 

 and of the lunar equilibrium tide, paragraph 28, the equation of the 

 latter (equation 16) becomes: 



u=y2(Ma'IER')a{S cos^ 6- 1) + %(MayER')a{5 cos^ 6-3 cos 9) (20) 



The second term of this equation, y2{Ma^lER'^)a(5 cos^ 6—3 cos 6), is 

 the "lunar equilibrium tide dependent on the fourth power of the 

 moon's parallax." 



Substituting the numerical values for the constants in the coefficient 

 of this term, this part of the tide has the value, in feet, of 



0.007(5 cos^ 6-3 cos 6) 



The factor (5 cos^ 6—3 cos 6) has a maximum value of 2 when 6=0, 

 decreases to —0.894 when 6=Q3°2&', 

 increases to 0.894 when ^=116°34' 

 and again decreases to a minimum 

 of —2 when 0=180°, repeating this 

 variation in the third and fourth 

 quadrants. This part of the equili- 

 brium tide is shown, on a greatly 

 exaggerated scale, in figure 8. 



It will be noted that the equili- 

 brium tide dependent upon the 

 fourth power of the moon's parallax 

 goes through three fluctuations from 

 maxima to minima as 6 goes through 

 a cvcle from to 360°; but that its ^'°'''^" 'i~'T"l°! 7'T''ZJ^^^^^^ °° 



" _ ' lourtn power of moon s parallax. 



maximum range is but one-quarter 



of an inch. It is superimposed upon and produces but an immaterial 

 distortion of the principal equilibrium tide due to the tliird power of 

 the moon's parallax, previously developed. 



Since the ratio of the radius of the earth to its distance to the sun 

 is but l/389th of its ratio to the distance to the moon, the equilibrium 

 tide dependent upon the fourth power of the sun's parallax is too 

 small to be considered. 



