MAGNETIC METHODS 213 



The vertical magnetic intensity at B, or AZb =z ATb cos x, which is obtained by 

 projecting the force ATb into the vertical direction. 



Hence : AZb = ATb cos :tr = -^ cos' x, (102) 



and since AZa = m/d^ we have 



AZb = AZa cos'' X or cos' x = — —■ (103) 



AZa 



By the original assumption of the problem AZb = Yz AZa. 



For this condition, cos" x — Vz AZa = J^ and cos x = J Y = 0.7937 and ;r = 37° 28' 



A 7. * 



AZj 



4 

 This gives : d = AB cot x = 1.305 ^5 = -j- /i5 



or ^5 = -^ d 



(104) 



In this equation d equals the depth to the pole. 



AB is the distance in feet on the graph between the abscissa at A, the point of maxi- 

 mum vertical intensity, and B, the point of ^ maximum vertical intensity. 



If B had been selected at 1/3 AZ maximum cos x = */~:r and d = 0.962 AB. This 

 formula is sometimes used, as are several others which are available, (cf. p. 186.) 



By these formulae, the depth to the pole is found, not the depth to the 

 top of the ore body. The AZ values of the curve represent the anomaly or 

 vertical intensity values as measured, from w^hich the average vertical 

 intensity has been subtracted. 



It is therefore necessary in surveying features which can be treated in 

 this manner to take readings at a sufficient number of stations away from 

 the influence of the dike or ore body, in order to insure a correct average 

 base value for the vertical intensity of the locality. These base readings 

 should also be taken at stations located in various directions from the body 

 under study. An incorrect average vertical intensity subtracted from all 

 readings would tend to increase or decrease the depth d as calculated. 



Type Curves. — Formulae have been given in the previous sections 

 whereby we may calculate the theoretical, or type, curves of AZ and AH 

 for magnetic poles at assumed depths and for bar magnet type situations 

 where both poles are considered. These are shown in Figures 76 and 79. It 

 is of note that these curves are symmetrical, which is characteristic of 

 vertical magnet-like tabular bodies. The cases referred to assume rod-like 

 bodies. Sheet bodies with infinite extent, at right angles to the sections 

 taken across them, also give symmetrical curves. The formulae by which 

 theoretical cases of this kind can be calculated have also been presented. 



It is of note that dip in the assumed tabular or magnet-like body 

 expresses itself, in part, by lack of symmetry. This is illustrated in Figure 

 81. Other efifects of dip will be treated in another section. 



