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Calcul de l'attraction d'un polygone horizontal de densité uniformeNormal access

Author: Jean Goguel
Journal name: Geophysical Prospecting
Issue: Vol 9, No 1, March 1961 pp. 116 - 127
DOI: 10.1111/j.1365-2478.1961.tb01124.x
Organisations: Wiley
Language: English
Info: Article, PDF ( 598.58Kb )

Summary:
The vertical component of the attraction exerted by a horizontal homogeneous polygon is obtained as the sum of terms proportional to the difference, for each of the vertices, between the external angle and its spherical perspective. A set of computation charts is presented, each for a fixed value of the angle of the polygon (22° 30′, 30°, 45°, 67° 30’ and 90°). These charts give the difference between the external angle and its spherical perspective as a function of the quotient of the distance from the sides to the vertical through the station over the depth. The chart for the right angle is an alignment chart, permitting a more accurate reading; the others are graphs in rectangular coördinates.

For a remote station the result would be obtained as a small difference between relatively large quantities, and consequently with a not quite satisfactory precision. For these stations it is preferable to assume the entire mass to be concentrated in the centre of gravity.


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