MAGNETIC DISTURBANCE 1385 
As a first approximation, for the mathematical solution of the mag- 
netic phenomena associated with the short string of casing, it was decided 
to regard the positive and negative effects as concentrated at the points 
f,e (Fig. 1), and to assume the ratio® of /L to be 0.833. By reference to 
Figure 5, it is seen that the essential characteristics of the calculated and 
experimental curves are in fair conformity, equal peak values being 
chosen for the purpose of computing the pole strength. The divergence 
toward the base of the curves may be largely ascribed to our assumptions 
regarding the distribution of magnetism within the casing, subsequent 
investigation leading to the opinion that more consistent results could be 
obtained if the poles were considered located at the extremities of the 
pipe. 
For the purpose of demonstrating the agreement between the theo- 
retical and observed values when/ = L, we place dZ = o in equation (5) 
and find that the calculated curve crosses the zero reference line when 
2 fi — gi b 
ey CLS (0) 
Also, by differentiating (5) we find dZ has a maximum value at x = 9, 
and a minimum when 
Be = 76 ie 
soa fess (10) 
a 
Substituting numerical quantities we find that dZ has a maximum 
value of 32,402 gammas directly over the casing, and becomes zero when 
x = 54 feet. The minimum value of —5 gammas occurs at a distance 
of ro1 feet from the pipe and at 200 feet the effect is —3 gammas. These 
data are in excellent conformity with the observed quantities, with the 
exception of the numerical value of the negative inflection point. 
So far, our comparison has been restricted to a short length of pipe 
in order to eliminate, as far as possible, the many uncertain factors asso- 
ciated with a relatively long string of casing. For this latter case, 
the relation between the calculated and the observed curves is illustrated 
in Figure 6, the required constants for the theoretical profile being found 
by solving simultaneously equation (5) for mean values of m and /, the 
corresponding anomalies and distances being obtained from the field 
data. The assumption was made that we may ignore the effect of the 
*This ratio is customarily supposed to lie between 0.80 and 0.875 for the ordinary 
type of bar magnet. 
103 
