A differential method for deriving magnetometer deflection‐constants

Abstract

For the computation of the horizontal component of the Earth's magnetic field from the observed angle of deflection of one magnet by a second in Lamont's first position a factor, intrinsically a function of the dimensions of the magnets employed, is required to correct for these finite dimensions. The so‐called “distribution‐coefficients” concerned in this factor are generally determined by means of a rather tedious computation depending on the data observed at three deflection‐distances. Theoretically the ratio of the sines (or the difference of the logarithmic sines) of the observed angles of deflection for any two distances is constant for a given instrument and pair of magnets; differential methods based on this theoretical condition are developed which simplify the computations required.The more exact form of the distribution‐factor, (1+Pr−2+Qr−4), is found to be less satisfactory in practice than the simpler form (1+P′r−2) for magnets which have been designed to make the value Q as small as possible (theoretically zero), on account of the greater sensitiveness to changes in the sine‐ratios of the factor containing both P and Q. The paper includes numerical examples and tabulations to show the application of the derived formulas to the determination of distribution‐coefficients, constants, and corrections on standard for a number of magnetic instruments of the Carnegie Institution of Washington.