periodic movement. The difference of level be
tween two points may be given by the formula:
AI k- akm sin 2Z cos (a A)
where k is a constant equal to 0.032 and 0.068
for the influence of the sun and the moon res
pectively; Z is the zenith angle; a and A the
azimuth of the alignment and the sun/moon
respectively (Jensen 1950, Waalewijn 1964). The
amplitude reaches an absolute maximum when
Z 45° and cos (a A)=\ for both the sun
and the moon at the same time (i.e. 1.5 pm). It
was considered that the necessary time of obser
vation was that short in comparison with the
time between two such amplitudes, that the
influence could be neglected as disappearing in
the "noise" of the measurements.
3. To establish the liquid reference surface, a PVC
pipe of a length of approximately 13 meter was
filled with distilled water. Windows in the pipe
every 2.6 meters made it possible to reach the
surface. Since the measurements involve con
ducting an electrical current through the liquid,
some chemicals were added in order to increase
the conductivity. Special care must then be taken
that the specific density is the same everywhere
in the solution. Differences in the specific density
may have a noticable local influence on the level
of the surface in the pipe.
4. The height of points above the surface is being
measured at different times and not simultane
ously at the same instant. Therefore the influence
of evaporation; of the fluctuations of the tem
perature of the air and of the liquid internally;
and of the air pressure should be assessed. By
the measurement of the various parameters and
the knowledge of the coefficients of expansion,
elasticity, compressibility of water, etc., it would
be possible to calculate the movements of the
liquid surface with the applicable formulae
(Waalewijn 1964, Sneddon 1974, 1975). The
check measurements made in the experiment,
however, were nowhere in agreement with the
results of the calculations, most probably
because the constants given in these formulae
were not applicable. The formulae indicate a
proportionality of the change in volume to the
differences in pressure and temperature. The
internal temperature differences in the liquid are
much more critical than the external ones. With
in the relatively short time of observations these
differences will be considered proportional to
time also.
The alignment set up is shown schematically in the
figure 2.
Problems on cohesion and adhesion, capillary
action in the liquid system are assumed to be solved
in the instrumentation as described in the next sec
tion. It should be mentioned that in many respects
use is made of the experiences as laid down by
Oostenrijk (1968) in his paper on the "Nivelmatic",
a multi precision hydrostatic levelling instrument
for the precise placing and checking of large machine
beddings, surface plates etc. in heavy industry.
2 Instrumentation (design and specifications by
Masée)
The height of a point is measured with two micro
meters (1), (2) as shown in the figure 3; one moving
upward with the zoneplate (3) attached, and the
other moving downward initially with a needle
attached to touch the liquid surface. The movements
of both micrometers are electronically controlled
with servomotors and switches from the observer's
place. The downward movement is measured
automatically with a counter that stops when the
needle touches the surface. The pointing of the
horizon at P
Ah
Fig. 1.
d i aphragn
(3)
zone plate
Iiquid
2.6 m
Fig. 2.
ngt 76
139
