Theory and practice of pendulum observations at sea
F.A. Vening-Meinesz
Nederlandse Commissie voor Geodesie 2,
Delft, 1929. 95 pages.
ISBN-13: 978 90 6132 002 9. ISBN-10: 90 6132 002 X. € 13.50
Summary
To facilitate the use of this publication, a short summary will be
given of the contents.
The first chapter contains the theory of the method for determining
gravity at sea by means of pendulum observations. The results of these
theoretical considerations, i.e. the formulae for the corrections and
reductions which have to be applied to the observed pendulum-period, are
put together in § 8. § 9 indicates the principal arrangement of the new
apparatus and the next paragraphs give some considerations about the
most practical initial conditions for the pendulum amplitudes and phases
in case this apparatus is used; sea-observations and land-observations
have to be treated separately. The conclusions are repeated in Chapter
II, which treats of the execution of the observations.
The first chapter is followed by several appendices: Appendix II
considers the case of observations carried out with a four-pendulum
Sterneck apparatus. As the observations and computations are troublesome
with this apparatus and take much more time, this case is not treated in
detail.
The other appendices contain further theoretical researches, which treat
of problems related to the subject: The first shows how the fundamental
equations may be solved more elegantly by means of imaginary quantities;
the third gives some details about negligible effects of the ship's
movements and the last treats the problem of three pendulums swinging
together on the apparatus while mounted on a fixed support, so that only
the sway of the apparatus interferes with the pendulum movement.
Chapter II gives a description of the apparatus, of the way to adjust it,
of the practical execution of the observations and a short note on the
determination of the sway.
Chapter III contains the methods of computation. The first five
paragraphs treat of the determination of the observed pendulum period
and of the reductions and corrections which have to be applied; § 5
gives an example of the complete reduction.
§ 6 is an appendix which contains a short summary of the methods of
computation, which are necessary if the observations are made with the
four-pendulum Sterneck apparatus.
The last paragraphs of this chapter treat of the determination of the
result for gravity and of the reductions which have to be applied to
this result.
According to the above summary he who wishes only to study the practical
execution of the observations and computations may confine himself to §
1, the first page of § 2, § 8 and § 9 of the first chapter, to chapter
II and to chapter III with the exception of 6 The theory of the method
is given by chapter I, while the appendices I, III and IV of this
chapter contain investigations on some related problems. Appendix II of
chapter I and § 6 of chapter III refer to the use of a four-pendulum
Sterneck apparatus.
Contents
Preface III
Summary of the contents 1
I. Theoretical Considerations and Formulae 3
Appendix I to Chapter I. Introduction of complex quantities 25
Appendix II to Chapter I. Deduction of other formulae for the correction for
deviation from isochronism and for the reduction to infinitely small amplitude
of the fictitious pendulum 31
Appendix III to Chapter I. Deduction of the formulae for the disturbances of the
fictitious pendulum, caused by the fact, that the knife-edges of the original
pendulums have relative movements, if the line connecting these knife-edges
deviates from its normal horizontal position 33
Appendix IV to Chapter I. Investigation into three pendulums swinging together
in case the apparatus is used on land 35
II. The apparatus and the execution of the observations 48
III. The computation of the results 72