124 



GRAVITATIONAL METHODS 



[Chap. 7 



N 



the error could be reduced on land has probably not been determined. In 

 any event, this method is not likely even to approach a modem gravimeter 

 in accuracy. 



2. Volumetric method (Haalck gravimeter'*) is illustrated schematically 

 in Fig. 7-27, where v and v' are the two volumes and z and z', respectively, 

 are the positions of the mercury menisci. If p is the pressure in the volume 

 V and p' is the pressure in the volume v', then the difference in pressure Ap 

 must be equal to the weight of the mercury column so that Ap = Az-5-g, 

 where 8 is the specific gravity of the mercury. To obtain sufficient sensi- 

 tivity, use is made of vessels of greatly increased section, of a lighter liquid 

 (toluol) on top of the mercury, and of small capillary tubes, C and C, for 

 reading the menisci. The increase in the accuracy is proportional to 



the ratio of the sections of the ves- 

 sel and the capillary (about 10,000 

 in the Haalck apparatus). A dis- 

 placement of the menisci by about 

 1 mm corresponds to a change in 

 gravity of one milligal. In the 

 first experimental model, the mean 

 error was ±10 milligals. The 

 lastest model is a quadruple ap- 

 paratus, has an accuracy of about 

 one milligal, is suspended in gim- 

 bals, and may be used on board 

 ship. 



3. Unastatized mechanical grav- 

 im£ters utilize the elastic force of 

 springs and the torsion of wires for 

 comparison with gravity. Me- 

 chanical, optical, or electrical 

 means of magnification are applied to obtain the necessary accuracy of 1 

 in 10 million. In a spring gravimeter, the deflection, d, is inversely pro- 

 portional to the square of its natural frequency, coo. Since the relation 

 Wo = \/c/m may be vTitten'^ oil = m- g/d • m, the variation of deflection d 

 and of the reading a with gravity (V = static magnification) is given by 



±. 



Fig. 7-27. Haalck gravimeter. 



Ad = — I and Aa = V-|, 



(1)0 Wo 



(7-29) 



»«H. Haalck, Zeit. Geophys.. 7(1/2), 95-103 (1931); 8(1/2), 17-30 (1932); 8(6), 

 197-204 (1932); 9(1/2), 81-83 (1933); 9(6/8), 285-295 (1933); 11(1/2), 55-74 (1935); 

 12(1), 1-21 (1935). Idem, Beitr. angew. Geophys., 7(3), 285-316 (1938). 



"See page 581, eq. (9-83). 



