508 G. Barus — Application of the Displacement 



It is this equation which suggests itself for the measurement 

 of the constant of gravitation which thus depends on quanti- 

 ties all easily measurable. It implicitly contains h, since i 

 refers to an eccentric axis and i 1 = i* + A 3 ; but i may be 

 found directly. 



The deviation 6 is given by (5). If, however, the device* of 

 two parallel mirrors, equisdistant (distance R) from the axis 

 of the horizontal pendulum, be used, and if light impinges on 

 either mirror at an angle of incidence / (the impinging and 

 reflected beams being always parallel), 



A2V' 

 6= „ r (11) 



where AiV 7 is the displacement of the micrometer. The hori- 

 zontal pendulum is in this case constructed symmetrically to 

 the vertical axis in the form of a balance beam, but somewhat 

 heavier on one side. 



Finally, the compound pendulum may be supported on a 

 cylindrical float, symmetrical to the vertical axis of the pen- 

 dulum and submerged in water or some other liquid. In such 

 a case, the mass of the compound pendulum may be reduced 

 in any degree without serious difficulty from capillary forces, 

 as will be shown elsewhere. Since the center of buoyancy is 

 in the vertical axis of the horizontal pendulum, the above equa- 

 tion needs but slight alteration. Let V be the volume of the 

 float, so that Vpg is the buoyancy. Apart from the tempera- 

 ture conditions, p = 1, and hence the above equations take the 

 successive forms, since (M— V)g is supported instead of Mg: 



W = \{M-V)gh$P (12) 



T' = (3I-V)ghcf>0 (13) 



The force at a distance R from the axis is, when the center of 

 gravity is at a distance h, 



FJ = ((M- V)g4>h/B)6 (14) 



Hence the force has been reduced in the ratio of M/(M — V) 

 for the same 6. One may also note that it is smaller, not only 

 as <f) is smaller, but as h/R is smaller. Hence a symmetrical 

 form of pendulum, like the balance beam, but slightly heavier 

 on one side, suggests itself for work on gravitational attrac- 

 tion, etc. 



It was not found difficult to reduce the weight of the pendu- 

 lum by flotation to 40 grams, i. e., about 31 times. Hence the 

 force per vanishing interference ring computed above would 

 now be 



* Barus, this Journal, xxxvii, p. 83 et seq., 1914. 



