Open AccessTHE DETERMINATION OF THE EARTH'S GRAVITATIONAL FIELD (Second Paper)
Author(s) -
Jeffreys Harold
Publication year - 1943
Publication title -
geophysical journal international
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.302
H-Index - 168
eISSN - 1365-246X
pISSN - 0956-540X
DOI - 10.1111/j.1365-246x.1943.tb00342.x
Subject(s) - harmonics , spherical harmonics , diagonal , gravitational field , term (time) , harmonic , gravitational constant , mathematical analysis , mathematics , compensation (psychology) , geodesy , geopotential , field (mathematics) , least squares function approximation , physics , constant (computer programming) , gravitation , classical mechanics , geology , geometry , statistics , quantum mechanics , computer science , pure mathematics , psychology , voltage , estimator , psychoanalysis , programming language
Summary The data used in a recent paper on the same subject have been rediscussed by a more sensitive method for detecting variations of gravity capable of being represented by spherical harmonics of low degrees. In the first place all cross (non‐diagonal) terms in the normal equations for the coefficients were neglected; in the second approximation the terms most strongly suggested by the first approximation were determined by the method of least squares. One second harmonic and three third harmonics, besides the terms included in the usual formulae, were found to be determinable. The variation shows no relation to the elevation of the surface and is inconsistent with accurate compensation. A new determination of the constant and the main ellipticity terms is made incidentally. No fourth harmonics are determinable on the data, but a suggestion is offered for the treatment of an independent term in Pp if occasion should arise.