Or if 0 is constant, then the soil bulk density can be obtained using

 p = -- [In ( x 09 [Av]


 Appendix B. Mathematical equations for soil water content
 (0) and bulk density (p) determinations using
 the dual-energy gamma attenuation method
 When gamma photons are transmitted through a soil core or column
either as a single collimated beam of dual-energy photons or as two
separate beams of monoenergetic photons with different energies, two
equations similar to equation [Aiii] in Appendix A result:
for gamma photons with primary energy a

 "-= exp {- x (/.p + /-wa 0)} [Bi]

and for gamma photons with energy c

 I
 -- = exp {- x (mop + pc 0) [Bii]
 1oc
These two equations can be solved simultaneously to obtain the two un-
known variables 0 and p, as reported by Soane (81)

 14a I y t sc 8C In
 0 = in i[Biii]
 X (GLsa ILwc 11sc Ilwa

 In In In()
 P 0 [Biv]
 X (ftsa itwe Ilse flva


 Appendix C. Mathematical description of experimental errors
 associated with determinations of soil water content (0) and
 bulk density (p) by gamma-ray attenuation methods
 Every determination of soil water content, 0, by the gamma ray at-
tenuation method has associated experimental errors. An infinitesimally
small water content determination dO, can be attributed to several
sources:

dO= dA (+ ) ( dp) + ( d, + d,,) [C

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