35
of arc.
The International Association of Geodesy recommended as early as
in 1950 to investigate its.effect on precise levelling networks.
4.4) Nonperiodic Effects
The last group of effects are the effects that do not have a
periodic character, at leas
25
3)
3.1)
INSTRUMENTATION AND ANALYSIS OF OBSERVATIONS
Tilt Measurements
To detect the tidal tilt one has to observe the variations of the
spatial angle between the local vertical (direction of gravity) and a line
thought to
represent theposition of the
21
( ).
d
u
'da
=
3
kW
.
3
= 2 k
aw
aa
Substituting these results back in (22) we get finally
1 AB ,;, _ _.._ k) aw _.1)
L:_  ( 1 + h l2_a_a
(22b)
where 'dW/'da can be interpreted as the negatively taken gravimetric tide
for the rigid earth.
Tidal
oth
16
What change in the potential W would now an
surface of the earth observe?
the
The potential W(A) obviously changes to W(B)
so that one would observe the difference W(B)  W(A).
be expressed as a summation of three terms: (i)
This difference can
W(, the
29
of. the individual components.
The amplitudes then can be compared to the
amplitudes of the theoretical tidal vawes and the values D and G computed.
Similarly, we can also compare the phases of the individual components to
get the phase lags of the the
18
Inversely, if the applied force is constant or secular, the earth responds
as an almost plastic body.
This is, of course, reflected in the fact
the the Love's numbers are also frequency dependent.
In the existing
literature this functional relationship
32
phases of the individual components by several tens of degrees.
In the
Bay of Fundy, Bristol Channel, SaintMalo Bay (southwest part of the English
Channel) and the Liverpool Bay, to name just a few locations, the actually
observed magnitudes of the ti
13
Table 2 continued
Symbol
Velocity
per hour
Amplitudelo5
Origin
(L, lunar; S, solar)
T2
29,958933
+ 2479
82
30,oooooo
+42286
30,041067

s
s
s
30,082137
+ 7858
L declinational wave
30,082137
+ 3648
s
R2
1
mK2
sK
2
354
major elliptic wave of 82
principal
1)
1.1)
TIDES OF THE RIGID EARTH
Tidal Force and Potential
To begin with, let us try to see how does the gravitation at
traction of a celestial body, say the moon (t), affect the earth.
To
trace the influence let us take two points  the center of gravit
3
This can be rewritten as
(4a)
and consequently
1/pl = 1/p y
Here y
1
1
(4b)
may be recognized as the. generating function for
Legendre's polynomials (see
y
1
1971],
2.22)
and we can write
00
=
2:
m=O
(B.)m P (cos Z)
P
m
(5)
where P (cos Z) are the L
10
cycle per day and we can thus see that the sectorial
raise to mainly semidiurnal variations,
constituent gives
the tesseral to diurnal variations
and the zonal to long term variations.
1. l1)
Decompo.@ion of Tidal Potential into Freg:uencies
_rhe class
8
where W is the tidal potential and g is the gravity.
The magnitude of the
uplift due to the moon is within< 17.8 em, 35.6 em> and due to the sun
from <8.2 em, 16.4 em>.
The total oscilation of the equipotential surfaces
can thus be as much as 78.0 em.
5
Let us first consider a second approximation taking the actual
distance of the surface point from the center of gravity (a) instead of
the mean radius of the earth (R).
We can rewrite the formula for the tidal
potential as
3
W ="= i+
K
M
2
l
a 3 (cos 2