DETERMINATION BY TORSION BALANCE afi 
the errors of the torsion balance surveys, then, are expressed in terms 
of gradient and not of Ag and the probable error of the torsion balance 
measurements will be in terms of gradient. But 




L 2 
ST= W and the other terms ere can be written: 
EC N-EC? 
or : 
L? L3 
—— 
N2 
F2 N- EC? 
If the terms—— of formula (7) are replaced by formula (5) is 
obtained, which gives the probable error in the torsion balance ob- 
servations in terms of gradient; that is, in Eétvés units, although the 
observed errors are in terms of Ag; that is, of cm. sec.” 
Formula (5) involves the two assumptions, first, that the error in 
calculation of Ag over a station interval is a linear function of the 
length of the station interval and of the error in the gradient and, 
second, that the error is independent of the magnitude of the gradient. 
Neither assumption is exactly true but in the present study no at- 
tempt has been made to analyze that more complicated variation of 
the error of torsion balance measurements. 
The original data and the calculated values of 
G2 IN; 
L 

are given in Table I. 
The “probable error” of the determination of the gradient at those 
twenty-eight hundred odd stations, therefore, is of the general mag- 
nitude of +2.2 E, but the “probable error” of the determination of 
the gradient may be different in different areas. If the surveys of 
Table I are grouped by the length of the interval between stations, 
the “probable error’ of the gradient varies considerably between 
groups. The various “probable errors” are given in Table II. They 
range from +1.5 E to +5.0 E. The corresponding ‘“‘probable error”’ 
in the individual traverses must have a yet higher range. The figure, 
+2.2 E, therefore, itself has a large “‘probable error” and only its 
general magnitude is of significance. Intuitively, the writer for years 
has estimated the common error of torsion balance observations of 
the gradient in the Gulf Coast region as of the magnitude of 1.5 to 
255 E. 
401 
