Formulas are derived for the magnetic anomalies caused by irregular polygonal laminas. These are used to obtain the three components of the magnetic anomalies caused by a finite homogeneously magnetized body of arbitrary shape. There is no restriction to the direction of magnetization; in general, it may not be the same as that of the earth's field. Total-intensity anomalies are also obtained. Use of these formulas in a computer program is discussed and illustrated by computing the anomaly caused by Caryn Seamount. Simplified formulas are presented for the anomalies caused by finite rectangular laminas. In addition to bodies of complex shape, the computer program can also be profitably used for computing the magnetic anomalies caused by bodies of relatively simple geometry. The second derivatives of the gravitational potential of a massive body, that is, quantities familiarly known as gradient and curvature in torsion-balance work and the first vertical derivative in gravity work are also obtained by this method.

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