CALCUL DE L'ATTRACTION D'UN POLYGONE HORIZONTAL DE DENSITÉ UNIFORME*

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.