the 68% of probability level, is equal to the square root of I. For small
increases of I, it is possible to make the following approximation;
 dl 1
 i-- [Cvii]

A fractional change in intensity measurement, dl/I, causes variations in
the determinations of density, dp, or thickness dx, or water content, dO.
By combining equations [Aiii] in Appendix A and [Cvii] as proposed by
Watt and Lawter (91) and with the statistical consideration of equation
[Cii] the error in water content measurements can be determined using

 a, = x, exp (pP + iPw0) [Cviii]
 xl,,i. -\ / L 2
where ao is the minimum resolvable change of water content.
 Similar to equation [Ci], the change in soil bulk density p, can be
analyzed using the following relationship

dp ( dA) +( d) + de)+( ,) d,)
 [Cix]
As expected, equation [Cix] reveals that the sources of experimental
errors associated with determinations of p are also the same ones that
influence determinations of 0. Spatial rates of change of p with respect to
A, x, tp., t., and p may be obtained by taking the respective partial dif-
ferentials for p in equation [Bi] in Appendix B:
 ap 1 [Cx]
 aA xAjS

 p X~1 x I
 Tx- + x0 [Cxi]
 Dp Ix, I ]xi
 -iW, I _I +i 1 J
 a= -I + xe -x [Cxii]

 YO 1 1- I 'a
 -= + xLT ,, [Cxiv]
Thus the minimum resolvable change, o,, of soil bulk density can be
calculated from the equation

 a =;xt, L 0-- exp (ap + G 4 wO) [Cxv]