ACOUSTICS AND GRAVITATION. 



(0 



where Q' V is the positive charge and potential in the top plate, at a distance 

 d' from the rubber surface at potential V and K' are the specific inductive ca- 

 pacity of the dielectric medium. Similarly, if Q"V" is the charge and potential 

 of the lower plate at a distance d" from V , a layer of specific inductive ca- 

 pacity K" lying between, 



w 



But 

 (3) 



the fixed charge on the rubber surface. 

 If the two plates are put in contact, 



(4) V'=V" 

 so that on combination 



Vti" 



n' n A a 



(5) ~^K" 



Furthermore, if the two plates thus charged are kept insulated and the top 

 plate is moved normally towards the lower a distance of y (figure 6), 



(6) 



AF being the potential difference thus produced and measured at the U-tube 

 electrometer taken as small in capacity in comparison with the electrophorus. 

 Hence, on inserting equations (5) and reducing, 



_ _ 



A(K"d'+K'd") 



It follows that y i = (constant) n; or the locus is a parabola. 



Among the experiments made to test this equation, it suffices to give the 

 data in figure 8, in which the displacement of fringes, n, is laid off vertically 

 downward, and the turns of the screw s in the apparatus figure 6 (pitch 

 one-twentieth inch) horizontally, the plates having been put m contact at 

 4 turns above the hard -rubber face (^' = 0.51 cm., d" = o.i6 cm., turn = 0.127 

 cm.). The zero of is heie arbitrary. When the plate moves down the para- 

 bolic form of curve is apparent. When it moves up from 4 turns, however, 

 the character of the curve soon changes. In other words, lines stray in the 

 latter case, whereas the stray field is caught to some degree in the former. 

 Furthermore, the capacity of the U-tube has been disregarded. Finally, the 

 unfortunate leak in the apparatus (fig. 6) is shown by a marked hysteresis- 

 like difference in the outgoing and return series, as indicated by the arrows. 



