418 



The condition which rnust be satisfied over the surface of the dubdle is that, apart fron 

 surface tension effects which are small when the diameter of the DubBls is greater than 2 cm., th 

 pressure inside must be equal to the pressure outside. At the vertex, the pressure is 

 (p + g cd + i pu^) and this nust therefore be the pressure of the air inside the bubble. The 

 expression (2.u) for the pressure is therefore satisfied all over the spherical cap if 



gR (1 - cos v] 



(2.5) 



Thi s equal ion is sat Isf ied for smal 1 values of i i f 



"g? " T" 



u = J ^ 



for, in that case. 



(2.6) 



1 im /'i - cos 0- \ 

 ..-oisin^.i, )" 



To see how far the theoretical relationship (2.6) is verified experimentally and to obtain further 

 data concerning the rise of bubbles, fourteen bubbles, rising in nitrobenzene, were photographed. 

 The results of the measurement of the films are summarized in Table I, where the first three columns 

 give the volume, V of the bubbles, the radius of curvature, R, near the uppermost point, and the observed 

 velocity of rise, J. The fourth column in the table gives the maximum transverse dimension, 2A of tne 

 bubble and the fifth column the angle 3;f„ =. sin"^ a/r. The sixth column gives the drag co-efficient, C^. 

 of the bubble, calculated from the equation 



C. X 77 A^ X i ,o u = 9 pv 



(2-7) 



The last column in the table gives the value :f Reynolds number. Re, referred to the fadius, 

 uf the maximum transverse section of the bubble, i.e.. 



(2.8) 



where V is the kinematic viscosity of the liquid. F': r nitrobenzene, the viscosity is 0.ni8 poises at 

 14°C., and the density is 1.20 gm./c.c, hence 1/ = 015 cm^/sec. 



"ubbles in ,Vi tro benzene. 



