DETERMINATION BY TORSION BALANCE 73 
That “probable error,” +2.2 E, is the composite error of a con- 
siderable number of factors. It arises: (a) from all instrumental errors 
in the determination of the crude gradient at the station, (b) from all 
errors in applying corrections to the crude gradient, (c) from errors 
in plotting gradient arrows on the map and from the crudeness of 
gradient arrows on a scale of 1 mm.=£ as the starting point for the 
calculation of relative gravity, (d) from inaccuracy in the use of the 
writer’s method of calculating relative gravity, and (e) from error 
arising from the fact that the interval between stations is not sufh- 
ciently close to give a true picture of the variation of the gradient. 
It probably also varies with the magnitude of the gradient; the data 
are not sufficient to study that variation. An actual error five times 
the “probable error’ should occur once in one thousand times, ac- 
cording to the theory of the “probable error.’’ Divergent gradients 
which depart vectorially much more than 5X + 2.2 E are moderately 
common. Such plainly aberrant gradient arrows were disregarded by 
the geophysicist in the calculation of relative gravity in the traverses 
from which the data of Table I were taken, and their weight, there- 
fore, was not felt in the calculation of that “‘probable error.” 
The ‘probable error’’ of the determination of relative gravity by 
good torsion balance surveys can be stated in a simpler and more 
practical form. The “probable error” of the determination of relative 
gravity by the torsion balance can be controlled within certain limits 
by variation of the station interval. Formula (3) can be rewritten: 
from: PE = \/n- pe 
8 
@) to: PE,, = V/n-SI- peve = 
the 
for the special case of the torsion balance. If the number of stations 
in a traverse of constant length is varied as the square of the variation 
of the “probable error” of the individual observations, the “probable 
error” of the determination of Ag for the traverse remains constant. 
In practice in good torsion balance surveys, the station interval be- 
tween stations is decreased in areas of irregular and erratic gradient 
arrows and is increased in areas of consistent gradient arrows. The 
“probable error’”’ of good ordinary torsion balance surveys in practice, 
therefore, should be independent of the station interval and should 
vary as the square root of the length of the traverse. If (S/- peuss) 
in formula (8) is maintained constant, then (m) will vary directly 
with the length of the traverse, and PF, will vary as the square root 
403 
