268 The Tide-generating Forces 



It is to be noticed that the luni-solar partial tide K x and K 2 are each composed of a lunar and 

 a solar part. The ratio of these parts is the same as for the ratio of the total tidal forces of moon 

 and sun (100:46). Hence, for K x 57-4 = 39-9+18-5, for K 2 12-7 = 8-7+4-9. 



The combination of the components K r (lunar part) +0 ± which have almost identical numerical 

 coefficients (39-9 and 41-5) gives the diurnal lunar tide. Neglecting the slight difference in the nu- 

 merical coefficient, we have 



sin(r— s)— sin(r+5) = — 2sinscosT: 



this is a diurnal lunar tide with an amplitude varying monthly. The maxima occur at s = 90° 

 and 270°, i.e. when the moon is in its greatest northern and southern declination respectively. 

 The combination of P x and K x (solar part) with 19-4 and 18-5, will give, because 



r+ s— h = t = solar time , 

 sin(r+ s— 2h) — sin(r+.s) = sin(/— //)— sin(r+ h) = —Is'mhcost. 



This is a diurnal solar tide with yearly variable amplitude; maxima occurs at h = 90° and 270°, 

 respectively, which is at the time of the solstices and the zero values at the time of the equinoxes. 

 This presentation, which can be extended to the K 2 - values, shows it makes equal sense to inter- 

 pret K y and K 2 either as seasonal variable solar tides or as monthly variable lunar tides. This is 

 because r+ s = t+ h. 



4. The Experimental Proof of the Tide-generating Forces 



If one had in the laboratory an absolutely rigid base, one could measure 

 the horizontal component of the tide-generating forces by means of the 

 oscillations of a pendulum, which coincides with the plumb-line when at 

 absolute rest (variations in the direction of the plumb-line). The vertical 

 component of this force could be measured by means of the time variations 

 in the weight of a small body (variations in gravity). These observations 

 should give the exact amount of the variations of these components, which 

 were derived theoretically from the system of tide-generating forces. The 

 variations in the plumb-line and in gravity observed in this manner are denoted 

 as tidal oscillations and these should fully agree, in case of an entirely rigid 

 earth, with the theoretical ones. 



The maximum value of these variations can easily be derived from the 

 equations (VIII. 10 and 11), along with the numerical values in (VIII. 7). For 

 the maximum acceleration in the horizontal and vertical direction relative to 

 gravity, we obtain 



in the horizontal in the vertical 

 for the moon : 8-57 x 10~ 8 1 1 -43 x 1(T 8 



for the sun: 3-78 x 1(T 8 504 x 10~ 8 



The maximum deflection of the plumb-line then becomes Axp = o" times hori- 

 zontal acceleration, which is 0-0177" for the moon and 0078" for the sun, 

 whereas the maximum disturbance of the gravity is 1 14 mgal for the moon 

 and 0050 mgal for the sun.* It is obvious that only extremely sensitive 



180° l 



* q" is = and 1 gal = 1 cm sec 2 , 1 mgal = 0001 gal. 



n sinl" 



