- 7 



233 



In one set of experiments undsr these conditions the drum camera was used and the Bubbles were 

 produced by discharging a Q.n fj. F. condenser charged to iiOSO volts. Two films, due to two separate sparks, 

 were taken and together they covered the period t = o to t = 120 milliseconds. The first film, covering 

 the period t = to t = 60 milliseconds, is shown in Figures 8a and 8b; the numbers to the left of each 

 photograph are (1) the number (v. Figure 3) of the particular contact of the timing pendulum which is 

 operative in the photograph; and (2) the value ^f t, calculated from the seperation of the photographs on 

 the film. The dark band, lying on the right-hand side of the photographs, is due to one of the leads to 

 the under-oil sparl^gap; the faulty reproduction cf photograph no. 2 is due to the fatt that it lies on the 

 j^in of the twL. ends .'f the film i;n the camera drum. The second film covered the period t c jo milliseconds 

 te t = 120 milliseconds and photi-graphs No. 17 to No. 22 are reproduced in Figure sc The values cf t are 

 net exactly spaced at intervals of 5 mi 11 isecnds owing to the fact that the timing pendulum was n.,t always 

 In exactly the same position relatively to the lower point of the gap when the spark went off. Some of the 

 sparks were as much as 1 millisecond late and one of them was nearly 1.5 milliseconds late. 



Owing to optical difficulties the field of view was not large enough to take in the bottom of the 

 bubble in its early stages. The radius was, however, taken as half the horizontal diameter, and the rise 

 of the centreabove the spark gap was taken as (the height of the top of the bubble above the spark gap) 

 minus (half the horizontal diameter). Figure 9 shows the radii (indicated by points surrounded by triangles) 



and the heights of rise (indicated by crosses) obtained in this way. The points are numbered i, 2 



on the same system as the photographs of Figure B, and the points given by the second spark are distinguished 

 from those given by the first by the letter 'a'. The points 12 and 12a dc not coincide, showing .that the 

 energy of the spark was different in the two cases. It will be noticed that the twc sets cf points lie very 

 well on smooth curves.' 



The naximum radius of the bubble was 3.15 cm., and since z = 6.5 + 6.05 = 12.55 cm., a /z - 0.25. 

 It has already been mentioned that this happens to be the value which corresponds with z' = 2.0, so that 

 I- = ^o''^'o " 12.55/2 = 6.27 cm. The corresponding value of w is W = 981 x 0.875 x 6.27" = I.32 x lo'^ ergs. 

 The factors by which Comrie's calculated values for z' = 2.0 must be multiplied are given by the equations 

 a = 6.27 a' and t = 0.O8O t'. 



For z'g = 2.0, Comrie gives the first minimum contraction at f = 0.67 which corresponds with 0.0535 

 seconds. This is considerably larger than the observed value shown in Figure 9, namely 0.0U5 seconds. 

 The difference may largely be explained by taking accotint of the effect of the free surface. According to 

 Herring, the period is reduced by the proximity of the free surface in the ratio / - \ 



where a is the mean value of a during the pulsation and h is the depth of the explosion below the free 

 surface. Taking a as 2.7 cm. (v. Figure 9) h = 6.05 cm., the predicted period of the bubble is O.0535 

 (1 - 2.7/2U.2) = 0.0475 seconds, which is close to the observed period of 0.0U5 seconds. 



Comparison of rate of rise with theoretical esttmato. . 



The calculation of the rate of rise, neglecting the effect of the free surface, cannot usefully De 

 compared with the observations because the critical point at which the minimum radius and consequent rapid 

 rise occurs is, as has been seen, 0.009 seconds earlier than that predicted by the simple theory. To take 

 account of the effect of the free surface, using the equations given in the Appendix, involves a great deal 

 of laborious calculation. Two simpler methods can be used. One is to take Comrie's calculated values of 



z' - z' for observed values of a, rather than for the values of t*; another is to calculate U = -dz/dt 





 directly from the observed values of a and t, using equation (1) of Report a, and then finding z by integrat- 

 ion. The values obtained by these methods are indistinguishable in the range shown in Figure 9. It will be 

 seen that until the bubble begins to contract the observed rise is not very far from the calculated rise, 

 but that the observed rate of rise becomes less than that calculated shortly after this. when the radius 

 begins to contract rapidly at t « 0.035 seconds the bubble begins to rise rapidly, but the rate of rise is much 

 less than that calculated on the theory which assumes that the bubble remains spherical. The probable 

 reason for this seems to be that the bubble ceases to be even a pprox irately spherical as It gets near its 

 minumum radius. It flattens on the underside and even becomes hollow there before reaching the minimum, as 

 Figures 5, 6 and photographs no. 7 to 10 of Figure sb show. 



Comparing Figures 7 and 9 it will be seen that the scatter of the points in Figure 7 is a 

 true measure of the variability of the energy of the bubbles produced by successive sparks. 



