HO GRAVITATIONAL METHODS

Torsion Balance Effects.—The torsion balance effects for an
infinite horizontal cylinder parallel to the 2/-axis can be shown by
integration of the effects for a sphere to be as follows:

74

(82)
(83)

r, — ^

(85)

m is the mass per unit length, or

m = TT/JV

Gradient.—For a gradient profile across a cylinder, \vo lake
the axis of the cylinder parallel to the (/-axis (Fig. 59) and

(86)

where

(87)

A curve for fgr(x/z) is given by curve 2 of Fig. 60.

Taking the same cylinder as calculated above (i.e., R = 3,000
ft., % = 5,000 ft., o- = 0,25) gradient effects at a few distances are

Distance x, ft.
x/z
/;/*/;)
(''/„., Kotvos units

0
0
0
0

2,500
«
0.64
48.0

5,000
1
0.50
37.0

10,000
2
0.16
12.0

By differentiating the expression for fyr(x/z) and equating to
zero, it can be shown that the maximum gradient occurs at a
distance