axis have been used on the negative side. The reason for this is that the contours 

 computed for the negative side of the y axis crowd in so close to the x axis 

 the map becomes inconvenient to use in this part. 



Tables 27-11, 27-111, 27-IV, 27-V contain coordinates of points to be used in 

 plotting the contours of c — log, (x + \/x 2 + y 2 + 1 j at intervals of 1/10 from 



c — .1 to c = 3.0. Table 27-V gives the coordinates of the points where the 

 contours cross the y axis. 



Y Y Y 



1 3 1 2 



Figure 27-7. 



The procedure followed in computing A z for semi-infinite vertical cylinders 

 or prisms is roughly the same as that used in the two dimensional case except 

 that the outline of the body is measured in units of the depth h. To compute 

 A z for a cylinder of finite length, the top being at a depth h t and the bottom 

 at depth h 2 , the computation is carried out for two semi-infinite cylinders, their 

 tops being at depth h t and h 2 respectively. The value of A z for the cylinder 

 of length (h 2 — hj) is then the difference between the two attractions of the 

 semi-infinite cylinders. If the outline of the cylinder falls partly above and 

 partly below the y axis, the computation for each of the two parts must be 

 carried out separately, that is, as though there were two different bodies each 

 bounded on one side by the y axis. 



For a sample calculation, let the given body be rectangular in cross section 

 measuring 300 feet by 200 feet on the sides and let the depths to its top and 

 bottom surfaces be 100 feet and 300 feet respectively. Two calculations must 



594 



