points indicated by dots on the outlines of the two bodies and the results 

 tabulated below. 



Large rectangle 



1.92 -1.28 



1.94 -1.35 



1.97 -1.42 



2.00 -1.48 



2.03 -1.54 



2.06 -1.59 



2.09 -1.65 



2.12 -1.71 



2.14 -1.75 



2.18 -1.80 



20.45 -15.57 = 4.88 



In the case of the large rectangle the value of y 2 — Ji is 3/10 units while for 

 the small rectangle its value is 1/10 unit. If we use 1 gm./cm. 3 for the value 

 of p and express h t and h 2 in centimeters, the value of A z for the body whose 

 vertical dimension is (h 2 — h t ) will be 



A z = kph t (4.88) (0.3) - &pM4.03)(.l) 



= (6.67 X lO" 8 ) (3048) (4.88) (0.3) - (6.67 X 10 ~ s ) (9144) 

 (4.03) (0.1) = 0.05 milligal 



Solid Angles 



The vertical component of attraction of a subsurface body may also be 

 computed by dividing it into thin horizontal slabs and supposing the mass of 

 each slab to be concentrated on a very thin lamina coinciding with the center 

 of the slab. The attraction component A z of each of the lamina is then 

 proportional to the solid angle subtended by the lamina at the point on the 

 surface where A z is to be computed. 



To compute the solid angle subtended by the lamina, we notice first that 

 A z is given by 



= k °H- 



dudv , (24) 



(u 2 + v 2 + h 2 f 12 



where a is the mass per unit area of the lamina and h is its depth. Since 

 r — (u 2 + v 2 + h 2 ) y* and cos0 = h/r (fig. 27-9), we may write the expression 

 for A z in the form 



596 



