The Tide-generating Forces 



263 



Fig. 112. The system of the horizontal component of the tide generating force at the surface 

 of the earth. The disturbing body is in the zenith of the point Z. 



3. The Harmonic Analysis of the Tidal Potential 



As a consequence of the orbital motion of the disturbing body and of 

 the diurnal rotation of the earth, the system of the tide-producing forces 

 relative to the earth is changing constantly. The distance of the disturbing 



a --w-s 



Celestial equator 

 Fig. 113. 



body M from the zenith depends upon its declination d and upon the geo- 

 graphical co-ordinates cp and A of the point B on the earth. In a spherical 

 triangle in the sky MPB (M = disturbing body, P = celestial pole, B = ob- 

 served point; see Fig. 113), 



cos d = sin0sinr5 + cos<£cos<!>cos(7 + A— 180°) 



if t is the real hour angle of the disturbing body (moon) in Greenwich, 

 counted from the lower culmination. If we introduce the complementary 

 angle (polar distances of M and B) 



A =90°-d and % = 90°-tf> 



