184 



GRAVITATIONAL METHODS 



[Chap. 7 



only readings n and no Uq . With deflections A from the torsionless posi- 

 tion, the equations are: 



C/. 



1 ^ 



= -^ [0.2351 (Ag - A4) + 0.3804(A2 - Ab)] 



1 



Uyz = -r- [0.7236(A3 + A4) + 0.2764(A2 + Ag)] 



D 



C/a = -[0.2351 (A3 - A4) - 0.3804(A2 - Ab)] 

 a 



} (7-54&) 



2C/x„ = -- [0.1382(A3 + A4) + 0.3618(A2 + Ab)], 

 a 



where the numerical factors represent combinations of trigonometric func- 

 tions, as given before, and where 



no = 



wi + na + ns + 714 + Wb 



4. Horizontal gradiometers and similar instruments. Because gradients 

 are more readily interpreted than curvature values, and since the latter 



are very erratic in certain types of 

 work (rugged topography, and irreg- 

 ular density distribution near the 

 surface), a number of attempts have 

 been made to design torsion balances 

 which furnish the gradients alone or 

 give them at least in fewer posi- 

 tions than are required to obtain 

 both gradients and curvature values. 

 This objective may be accomplished 

 by balance beams of different designs 

 or by suitable combinations of stand- 

 ard beams. In any beam with sym- 

 metrical mass distribution the in- 

 fluence of the curvatures is zero. 

 If one of these masses is placed at 

 a different elevation, the beam will 

 be affected by the gradient forces 

 alone. In the gradiometer of Shaw 

 and Lancaster-Jones three masses 



Fig. 7-61. Gradiometer. R, Damping 



ring; p, arm; m, masses (after ^^ j_ ggi. Instr., 49(11/12), 1-20 (Nov. 



Lancaster-Jones). and Dec, 1932). 



