LIQUIDS AND AEEIED EXPERIMENTS. 



49 



respectively, t the absolute temperature, R the gas constant for air, and g 

 the acceleration of gravity. This equation applies when the uncharged 

 diver is just about to sink, or is instantaneously in unstable equilibrium. 



If, now, other things remaining the same, the diver is charged to potential 

 V, and D is the distance apart of the plates of the condenser, A the area of 

 the movable disk, and / the electric pressure, 



F = 3ooDV87r/ 



(2) 



where V is given in volts. 



The effect of the charge is to keep the diver suspended, ■/. c, to virtually 

 reduce the weight Mg hy JA. More water will have to enter to just float it. 

 Hence H must be increased to H', while h changes slightly. Hence 



y , rj, Pm = RntT 



"*" P, (Mg-fA)(i- P J Pt ) 



It follows from equations (i) and (3) that 



Mg {h'-h) Pw +{H'-H)p m 

 J A h' Pw +H' Pm 



(3) 



(4) 



As a rule h' — h, which refers only to the difference of level of the liquid in 

 the diver, in the charged and uncharged states, may be neglected, and if R 

 is the radius of the disk, A = irR 2 , so that 



f= 



Mg H'-H 



tR 2 H'+hpJp m 

 If this be substituted in equation (2) the result is finally 



T/ D 



V = 2>oo — 



8Mg 



H'-H 

 H'+hpJp, 



(5) 



(6) 



It is interesting to obtain an estimate of the numerical value of H' — H for 

 a diver which, when charged, floats at about atmospheric pressure. In the 

 apparatus, fig. 15, M is about 35 grams and R about 3.5 centimeters. Hence 



H'-H = 3.8Xio~ s V 2 /D 2 



(7) 



and roughly the data given in table 1 2 apply, the numbers not defined being 

 H' — H in centimeters. 



Table 12. 





7=io 



V= 100 



V= 1000 



V= 1 0000 



.D = o.oi cm. 

 D = o. 1 cm . 

 D = 1 cm . . . 



4X10- 2 



4 

 4X10- 2 



4 

 4Xio- 2 



4 



