. Early geophysical papers of the Society of Exploration Geophysicists . 8 /ECn\> N,+ â â â¢(-JA, (S)PEUSZ = " where: ECi, EC?., ⢠â ⢠ECn are the respective errors of closure in Ag of n closed torsion balance traverses numbered from 1, 2, ⢠⢠⢠to n; N\, N2, ⢠⢠⢠Nn are the respective number of stations in those traverses; Lh L2, ⢠â â Ln are the respective lengths of those traverses in centimeters; n is the number of traverses; and PEusz is the probable error in the dimensions of the gradient. The formula is adapted from Merriman's formula:1 (6) /1 / </i2 d2* dn*
. Early geophysical papers of the Society of Exploration Geophysicists . 8 /ECn\> N,+ â â â¢(-JA, (S)PEUSZ = " where: ECi, EC?., ⢠â ⢠ECn are the respective errors of closure in Ag of n closed torsion balance traverses numbered from 1, 2, ⢠⢠⢠to n; N\, N2, ⢠⢠⢠Nn are the respective number of stations in those traverses; Lh L2, ⢠â â Ln are the respective lengths of those traverses in centimeters; n is the number of traverses; and PEusz is the probable error in the dimensions of the gradient. The formula is adapted from Merriman's formula:1 (6) /1 / </i2 d2* dn* \ P£ = (- + -+...+-) where PE is the probable error of each measurement with a surveyor's chain. It is assumed that the length of (n) lines (1, 2, ⢠⢠⢠n) has been measured with the chain and is expressed in chain lengths; and that two measurements of each line were made. The respective differ- ences between those duplicate measurements of each line are repre- sented by d\, d2, â ⢠⢠dn and the length of the respective lines in chain lengths by L\, L-t, ⢠⢠⢠Ln. PE, then, is the probable error of any one of the many single measurements of the chain. The probable error of the measurement of each line, then, can be calculated by formula (3) from the PE which has been obtained by formula (6), and from the number of individual consecutive measurements with the chain which were necessary to measure the length of the line. The measurement of Ag by the torsion balance around a series of closed traverses is comparable to that duplicate measurement of each of a series of lines with a surveyor's chain. Each duplicate measure- ment of the length of the line may be regarded as a closed traverse which will consist of as many single measurements with the chain as the length of the line in chain lengths. A torsion balance traverse which is composed of N successive stations may be regarded as N consecutive measurements of a line c
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