ln( lTa Al =x [Di]

 -\n (IT)_ sc /wcL 0
This form of the equations clearly reveals that the precision of water
content (0) and bulk density (p) determinations depend strongly upon
the precision of measured values of soil and water mass attenuation co-
efficients.
 Using equations [Cxviii] and [Cxix] in Appendix C, Mansell et al.
(58) calculated contributions to standard deviations in determinations
of 0 and p due to random error in measuring attenuation coefficients
(Fig. 9) for the special case of a soil column with thickness of 10 cm
known to within 0.01 cm, bulk density of 1.50 g/cm3, attenuation co-
efficients of 0.2500 () and 0.0780 ( C,) cm2/g for 60 and 662 KeV
gamma rays, and with nonswelling properties. Attenuation coefficients
of 0.2040 (p,) and 0.0857 (p,) cm2/g for water were used for 60
and 662 KeV gamma rays. Count rates through the empty soil container
were 4.6 x 106 cpm for 241Am and 3.2 x 106 cpm for '37Cs. For
equal precision of measurement in the four attenuation coefficients for
soil and water, the standard deviation for soil water content was essen-
tially constant at about 0.8% water content for precisions greater than
2 x 10-5 cm2/g in the attenuation coefficients, but for precisions less
than 1 x 10-4 cm2/g, the standard deviation for 0 increases exponen-
tially. For precisions of the attenuation coefficients within the range from
2 X 10-6 to 1 X 10-4 cm2/g, values for the standard deviation for 0
were observed to occur within the interval from about 0.8 to 1.1%
water content. Values of the standard deviation for p over this practical
range of precision occur within the interval from approximately 8 to 9
mg/cm3. The intervals indicated for each point on the standard devia-
tion curves for 0 and p show the small but significant influence of in-
creasing 0 from 3 to 40% water content by volume with p remaining
constant. Figure 9 implies that the precisions of measurement in t,,s for
60 KeV photons and soil, E,, for 662 KeV and soil, ju, for 60 KeV
and water, and .,we for 662 KeV and water, have equal effects upon the
standard deviations for 0 and p. Gardner et al. (36), however, showed
that the precision of I A, has a much greater influence upon the standard
deviations for 0 and p than either of the precisions of measurement for
ASsa, Lwa, or M.... For example, where the precision of ,sa, s, !1a, and
,, are each 10-3 cm2/g the standard deviation for 0 has a value of
7.27%, but by simply changing the precision for p,. to 10-4 cm2/g, the
value of the standard deviation decreases to 2.65%.