axis vertically downward. With axes chosen in this way the direction cosines are 

 (l,o,n) and the potential 



V = I f f f l — ^— (— ) + n — — (— ) dudvdw (47) 



J J J | 3m r 9m; r 



The field component H z {x,y,z) will then be given by 



H.{x,y f z)=lfff" 



( — ) + n ( — ) 



'du'dw r ^>w 2 r 



dudvdw, (48) 



the integration between the limits h and co being carried out with respect to w. 

 The result of this step is 



At the point (o,o,o) this becomes 



«• c. ». «) = ' / f (u . +VVV' *"** <50) 



If we measure u and i> in units of h and take as the field of integration 

 the narrow rectangle shown in Figure 27-7 we get approximately 



Hz = I \W + D (*» 2 + ys* + D 1 /* ~ W + yS + D 1 '*]®' ~ Jl) 



\ nxj / I , _ v 



|(j/ + 1) ( Xl * +y s 2 + D 1 ' 2 ( Xl '+y 3 2 + l) ll2 \ {y " yi) 



(51) 

 The function to be mapped is 



/r ^ _ n^ J 



' {X,y) " (y 2 + l) (x 2 +y 2 + l) 112 {x 2 +y 2 + l) il2 



Table 27-VIII gives values of {x,y) which may be used to map this function 

 for I inclined at an angle of 60 degrees. A contour map plotted from this table 

 is shown in Figure 27-14. It may be used to compute fields of vertical cylinders 

 or prisms in a way similar to that described for computing the vertical com- 

 ponent of attraction A z of a vertical cylinder or prism. 



606 



