DETERMINATION BY TORSION BALANCE 69 
EC EC 
y/ ee Ge Ge) 
Ly Ls Ln 
(5) PEue = 0.6745 ————————— 
n 
where: 
EC,, EC2, - - - EC, are the respective errors of closure in Ag of n 
closed torsion balance traverses numbered from 1, 2, -- - ton; 
Ni, N2,---N, are the respective number of stations in those 
traverses; 
I,, L2,--- LZ, are the respective lengths of those traverses in 
centimeters; 
n is the number of traverses; and 
PEyzz is the probable error in the dimensions of the gradient. 
The formula is adapted from Merriman’s formula:! 
3 pae : \/- 1 d? dn? 
6) ie Ge Ls a a =) 
where PE is the probable error of each measurement with a surveyor’s 
chain. It is assumed that the length of (z) lines (1, 2, - - - 2) 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 di, do, - - - d, and the length of the respective lines in chain 
lengths by Li, Le, - - - L,. 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 NV 
consecutive measurements of a line comparable with those consecu- 
tive applications of the surveyor’s chain to obtain the length of those 
lines. The error of closure of Ag, (EC), of a closed torsion balance 

1 Op. cit., p. 103. 
399 
