36 EXPERIMENTS WITH THE DISPLACEMENT INTERFEROMETER. 



If F, as before, is the force at the center of gravity, the corresponding force 

 at the grating, a distance R from the center, is 



(10) F R 



since <f> is given by equation (6). This equation implicitly contains h, since i 

 refers to an eccentric axis and 2 =' 2 o+^ 2 ; but i may be found directly. 



The deviation 9 is given by (5). If, however, the device* of two parallel 

 mirrors, equidistant (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), 



where AA/' is the displacement of the micrometer. The horizontal 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 or not to the vertical axis of the pendulum and submerged in 

 water or some other liquid. In such a case, the mass of the compound pen- 

 dulum may be reduced in any degree without serious difficulty from capillary 

 forces, as will be shown below. If the center of buoyancy is in the vertical 

 line passing through the center of gravity of the horizontal pendulum, the 

 above equation needs but slight alteration. Let V be the volume of the float, 

 so that Vpg is the buoyancy. Apart from the temperature conditions, p=i, 

 and hence the equations take the successive forms, since (MV)g is sup- 

 ported at the center of gravity, instead of Mg, 



(12) W f =~ 



(13) r 



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

 distance h, 



(14) F' R = ((M-V)gvk/R)6 



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 <p 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 pendulum by 

 flotation to 40 grams, i.e., about 31 times. Hence the force per vanishing 

 interference ring computed above would now be 



F' R = 2 X io- 3 /3 1 = 6 X ic- 5 dynes, roughly. 



This would be equivalent to the attraction of two 30-gram weights at i cm. 

 of distance. 



*Barus: Am. Journ. Sci., xxxvn, pp. 83 et seq., 1914. 



