I
 where A = In T Under ideal or perfect conditions the parameters
 x, p, t,, and A, may be considered to be constant such that the second,
 third, fourth and fifth terms on the right hand side of equation [Ci] should
 be negligible. For such an ideal case a measured change in water con-
 tent, dO, would be attributable completely to a change in the logarithm
 of the ratio of attenuated and unattenuated radiation intensities dA. In
 other words, an increase in the measured 0 would be attributed to a de-
 I
 crease in the relative radiation intensity, / Under nonideal or actual
 laboratory conditions, a measured change in soil water content will still
 be primarily attributable to a measured change in A, but changes in x,
 p, t,w and p,s will contribute errors to the measured change dO. Gardner
 and Calissendorf (36) have examined several components of equation
 [Ci] which contribute errors to measurements of soil water content by
 the single-energy gamma radiation attenuation method. They concluded
 that precision in the measurements of x, pw, 1, and p are particularly
 important to determinations of water content. Spatial rates of change
 of 0 with respect to A, x, p/,, p, and p may be obtained by taking the
 respective partial differentials for 0 in equation [Aiv] in Appendix A:

 30 1
 [Cii]
 aA Xyp,,


 X I X2 [I x [Ciii]

 30 1 (1)+ a


 x. + xP [Cv]
 19 -1 r, a xI,


 1\ 31 x [Cvi]
 dp x/w I -p gw J

Thus one may easily perform a sensitivity analysis for 0 determinations
by solving equations [Ci] through [Cvi] for given values of 1, 1o, x, IAw,
A,, and p and then using these solutions to solve equation [Ci] for dO
Such analyses show the importance for precise measurements of 1, x, t,,
.s, and p.
 Experimental measurements of I and I, are subject to errors due to
the statistical fluctuations in the radioactive disintegration events. Dur-
ing the measurement of gamma radiation intensity I, the uncertainty, at
 48