MOTION OF THE GAS SPHERE SOS 



hydrostatic pressure above the hquid to a small fraction of atmospheric 

 pressure.^ In order to obtain the closest comparison with the theory 

 so far outlined, one series of experiments was carried out under a vacuum 

 to minimize the effect of a surface, and the spark was produced at a 

 depth which gave amax = 3.7 cm., Zo = 6.01 cm. The ratio a^^^i^/Zo 

 = 0.61 corresponds to zj = 1.0 in the calculations of Comrie and 

 Hartley, and the experimental values of radius and rise versus time 

 should therefore be represented by the curves for zj = 1.0 in Fig. 8.8, 

 provided the scahng factors L and t/f of the theory are chosen as 

 L = Zo = Q.l cm. and t/t' = Vl/g = 0.079. The values of lengths I 

 and time t are then given b}^ 



I = 6.05 V, t = 0.079 t' 



The measured radii and migrations are compared with the theory 

 in Fig. 8.10. Although the radius values show considerable scatter at 

 longer times, they are seen to be in rather good agreement with theory, 

 as are the measured upward displacements. The data thus provide a 

 very satisfactory confirmation of the gravity theory. 



As already mentioned, the case just considered corresponds to 

 shallower depths than can ordinarily be realized without large effect of 

 the free surface. In another series of records, Taylor and Davies ob- 

 tained the radial and vertical displacements for a bubble formed at the 

 same depth, but with a surface pressure equivalent to a depth 6.5 cm. 

 for the oil used. The resulting motion therefore corresponds to a large 

 scale experiment at atmospheric surface pressure and the charge fired 

 at a depth of (6.05/6.50) X 33 = 31 feet. The greater pressure at the 

 depth of the bubble leads to a smaller observed maximum radius, 

 am = 3.15 cm., and the value am/zo = 3.15/(6.05 + 6.50) = 0.25 corre- 

 sponds to the case zj = 2.0 calculated by Comrie and Hartley. The 

 scale length L required to convert the calculated values to experi- 

 mental conditions is then L = Zo/Zo' = 6.27 cm., and hence a = 6.27 a', 

 t = Vl/g t' = 0.080^', where a' and t' are calculated nondimensional 

 values. Under these conditions, the bubble remained spherical during 

 the first expansion, then flattened and became concave on its lower sur- 

 face as it contracted. The subsequent expansions restored the sym- 

 metry to a considerable extent, and the bubble moved upward toward 

 the surface with considerable velocity. 



5 In the experimental arrangement employed by Taylor and Davies, the bubble 

 spark is produced in a cylindrical glass tank by discharge of a condenser initially 

 charged to 4000 volts. In some of the experiments, transformer oil of low vapor 

 pressure was used as a fluid instead of water, in order to prevent boiling at the bubble 

 surface in its low pressure, expanded phases. Illuminating sparks at intervals con- 

 trolled by a pendulum timing device gave a series of exposures on a film mounted on 

 a rotating drum. Optical distortion by the walls of the cyhndrical tank was pre- 

 vented by attaching plane-walled auxiliary tanks, also filled with oil. 



