CiiAr. 7] 



GRAVITATIONAL METHODS 



85 



III. GRAVITATIONAL CONSTANT; GRAVITY COMPENSATOR; 

 GRAVITY MULTIPLICATOR 



The mutual attraction of all masses is governed by Newton's law of 

 gravitation which states that the attraction of two masses mi and rriz is 

 proportional to their product and inversely proportional to the square of 

 the distance between them, 



F = 



k'Tni'Trii 



(7-1) 



(d) 



8:^=-— 



AfO 



o— o 



o 



M 



where F and k are measured in dynes if m is in grams and r in centimeters. 

 When mi = mz = r = 1, F = k; hence, k (called the gravitational constant) 



is the force of attraction between two equal 

 masses of 1 g. each at a distance of 1 cm. Its 

 dimension in the C.G.S. system is gr~^-cm'- 

 sec~"; although it is exceedingly small (about 

 one 15 billionth part of gravity), it may be 

 determined accurately from the force exerted 

 by large masses upon small masses at a known 

 distance. 



The Cavendish torsion balance is generally 

 used in making these measurements. The 

 force may be determined statically (by meas- 

 uring deflections) or dynamically, that is, by 

 observing the period of oscillation of the 

 balance beam under the influence of known 

 masses. Fig. 7-3a shows arrangements of de- 

 flecting masses M in reference to the deflected 

 beam of the length 21, carrying two small 

 masses m at its ends. The angle of deflection, «p, is measured at great 

 distances from the balance with telescope and scale. Sometimes the dou- 

 ble deflection is observed by revolving the masses M about a horizontal 

 axis to the other side of the small masses. For the single deflection, the 

 gravitational constant follows from 



o 



( 



o 



Fig. 7-3a. Arrangements 

 for the static and dynamic 

 determination of the gravita- 

 tional constant (after Heyl). 



A; = 



T<pr 

 2Mml' 



(7-2) 



where r is the torsional coefficient of the wire, and r the distance between 

 M and w. A correction is applied since, for very small distances, the 

 mass of M may not be assumed to be concentrated in its center of gravity." 



" P. R. Heyl, "A Redetermination of the Newtonian constant of Gravitation," 

 Proc. Natl. Acad. Sci., 13(8), (Aug., 1927). 



