DETERMINATION BY TORSION BALANCE AS 
with the shorter station interval (Table II). That larger “probable 
error”’ of the individual observations in the traverses with the shorter 
station interval has been compensated by the use of that shorter 
station interval; and the ‘“‘probable error” of the traverse as a whole 
is no greater for those traverses with the shorter station interval than 
for those with the longer station interval. The “‘probable error’”’ of 
determination of relative gravity by those 45 traverses is 0.4 milledyne 
per 10 kilometers of traverse without regard to the station interval; 
and the actual error of closure, with two exceptions, is less than 0.9 
milledyne and with only five exceptions, is less than 0.75 milledyne 
per to kilometers of traverse without regard to the station interval. 
The “probable error’ of the determination of relative gravity 
between two places by torsion balance surveys depends in part on 
the number of torsion balance traverses which connect the two places, 
decreasing inversely as the square of the number of equally good 
traverses. Key places in torsion balance surveys in general are con- 
nected by at least two traverses, and in many surveys are connected 
by a net of traverses. Different weights in general should be given 
the different traverses in the calculation of the relative gravity be- 
tween the two places and in the calculation of the “probable error’’ 
of that determination of the relative gravity. But that “probable 
error’ in practice probably will be 1/1/2 to 1/+/3 times the “‘probable 
error” of the determination of the relative gravity by a Single trav- 
erse. The “probable error” of the determination of relative gravity 
between key places within the surveys of those 45 traverses, therefore, 
should be (1/+/2 to 1/+/3) times o.4 milledyne or 0.30 to 0.25 mille- 
dyne for places 10 kilometers apart along the route of the torsion 
balance traverses. For an airline distance of ro kilometers between the 
two places, the corresponding “‘probable error” in practice should 
be 0.7 to 1.0 times the ‘‘probable error’’ of the determination of Ag 
by an airline torsion balance traverse between the two places and, 
therefore, should be 0.3 to 0.4 milledyne. 
Shrewd adjustment of errors in those 45 traverses presumably 
has reduced the “‘probable error’’ of those determinations of relative 
gravity below the figures of the preceding paragraph. The error of 
closure in Ag in torsion balance traverses commonly is caused not 
only by the cumulative effects of small, or moderately small, errors 
at each set-up but also by a few large errors. A skilled interpreter 
commonly can recognize the weak spots in which those errors are 
mostly likely to have come in; by disregarding or adversely weighting 
405 
