Theory and practice of pendulum observations at sea.
Part II. Second order corrections, terms of Browne and miscellaneous
subjects
F.A. Vening-Meinesz
Nederlandse Commissie voor Geodesie 6,
Delft, 1941. 89 pagina's.
ISBN-13: 978 90 6132 009 8. ISBN-10: 90 6132 009 7. € 13,50
Summary
Chapter I contains the theoretical investigations about the effect of
the accelerations of the pendulum apparatus on the gravity results. § I
treats of the effect of the horizontal component perpendicular to the
swinging plane of the main pendulums, § 2 of that of the second
horizontal component, § 3 of that of the vertical component and § 4 of
the rotational effects. In all cases the effect has been determined up
to the terms proportional to the square of the accelerations; there is
no doubt that the terms proportional to the third power are negligible.
In § I we shall also have to deal with the equations of motion of the
damped pendulums of the old pendulum apparatus which have not been
published in the paper of 1929; we need them for the investigation of
the effect of the accelerations on these pendulums. In § 5 we have
separately discussed the disturbing effects for observations made in
harbours at the surface of the water.
Chapter II deals with the determination of the vertical and horizontal
components of the accelerations. After an introduction in § 6, § 7 shows the
way the vertical accelerations may be derived from the records of the main
pendulums. These accelerations can, therefore, be determined for all the old
observations. In § 8 a method is developed for determining the horizontal
accelerations; this can be done by means of pendulums of very long period.
At the end of this paragraph some general considerations follow about the
determination of the total second order correction and § 9 gives a summary
of the formulas of the preceding two paragraphs. § 10 treats of the new
apparatus constructed for the determination of the horizontal accelerations;
it contains two long period pendulums swinging in planes perpendicular to
each other, one for each component.
Chapter III deals with the problem of determining the corrections for the
old observations. For doing this we have to make suppositions about the way
the horizontal and the vertical component of the acceleration are related.
By assuming the wave-theory of Gerstner or Stokes to be valid and by
supposing that the apparatus describes circles in a vertical plane in the
same way as the water-particles, we find such a relation and this makes it
possible to deduce the complete effect of both components from; the data
about the vertical component alone; these can be derived from the old
records. The study of the ship's and wave-movements is dealt with in § 11,
and § 12 gives the results for these movements derived from the experiments
during the voyages of Hr. Ms. 0 12, 0 13 and 0 19. Besides getting thus a
base for the computation of the corrections for the old pendulum results, we
likewise obtained data regarding the theories about the wave-movement. § 13
gives the results for the corrections of the old pendulum observations of
the stations nos 33 - 486 published in 'Gravity Observations at Sea, 1923 -
1932', Netherlands Geodetic Commission 1934. These corrections have been
derived according to the methods described in this publication.
Chapter IV deals with other problems concerning pendulum observations at
sea; § 14 treats of the adjustment of the old pendulum apparatus and § 15 of
methods for determining the difference of the pendulum-periods and of the
correction for sway.
In this paper we shall refer to the previous publication: 'Theory and
Practice of Pendulum Observations at Sea' as the "publication of 1929".
Contrary to what has been adopted there, and to what is usually done, we
have indicated by T in this paper the complete period of the
pendulums; i.e. the time of a double swinging instead of that of a single
swinging. For the three components x, y and z of the acceleration we adopted
the sign of the inertia forces of d'Alembert working on the masses of the
apparatus because of the translational movement of the system of coordinates
carried along with the middle knife-edge of the apparatus. So the components
of the acceleration of this knife-edge with regard to a fixed system of
coordinates are -x , -y and -z.
Contents
Introduction 1
Summary of the contents 4
I. Theoretical Investigations of the effect of accelerations 6
II. The Determination of the Vertical and Horizontal Accelerations 26
III. The Determination of the Second Order Corrections for the Old Observations
30
IV. The adjustment of the pendulum apparatus and other subjects 81