458 .,_ 



For the purpose of cunputat ion, a variable x was introduced, defined by:- 

 t dt 

 a '2 



In fact, in the Tables the quantities involved are defined in terms of equal intervals of 

 X, which obviously increases continuously with valuL'S of t, although the corresponding values of 

 t are given. The computations were carried out to the point where the equations ceased to have 

 any physical maning owing lo the radius of the bubble Decerning greater than the distance from 

 the model, (in the case of 'test 50, this happened just before the first minimum of the bubble 

 and the equations would have broken down in any case). As regards the accuracy of the solutions, 

 the following should be noted:- 



(a) ' warning must Be given about the interpretation of the computed figures. 

 In socre cases more figures than are justified have been retained in order 

 to keep a fixed number of decimals. The computer is fully aware of this 

 and precautions have been taken accordingly. 



(b) It is realised that u decimals in a and z are meaningless but it is 

 essential to keep this number of figures in order to comprehend the full 

 b^'.haviour of the solution and to understand the structure of the differential 

 equations. No great pains have be:n taken to maintain this accuracy, though 

 owing to the inherent stability of the equation for a, the last figure should 

 be reasonably good, even to the end. 



The tibUs give - for the rigid case 3, t, z, and - for the case where there assumed to 

 be a source ji, t, z, h, v. 



Discussion of Results . 



It win be seen by reference to Tables 1 and 2 and Figures 1 and 2 that the actual effect 

 of the plate motion on the bubble appears to be fairly small. In fact from Figure 1 it appears 

 that the effect of the mobility of the plate has not appreciably affected the depth of the centre 

 of the bubble. This may be due to the fact that over the greater part of the period under 

 consideration, i.e. from t = .02 to t = .17, the motion of the plate is comparatively small, the 

 bubble being fairly large over this time. As is well known, the bubble acquires momentum, chiefly 

 when large, and at this time the plate is practically stationary. The motion of the plate has 

 little effect on the radius. The maxima occur as far as cjn be seen practically at the same time 

 and the maximum radius is diminished by about 2% by the plate being asstmed to be non-rigid. 



In both cases the bubble begins to flatten itself against the target before the minimum 

 is approachrd although at this time the approximations erase to be valid in any case. 



Considering Table 2 and its graphical representation Figure 2, it may be seen that, 

 although the plate has sprung back, and has even come back beyond its original position, the effect 

 on the bubble is somewhat the same as in the case where the plate remained dished inward. 



The differences between the rigid case and the moving plate are very sligt.t, as regards 

 the movement of the bubble, and less than the probably accuracy of the theory. This might be 

 expected as the subsequent movement towards the plate is governed mainly by the momentum constant. 

 This agrees with photographic observations of the bubble moving towards the box model when a 

 rigid plate theory gave excellent results for both -rj inch and -rz inch plate. 



It should be noted that in the actual experiments the Box Model and charge are at the 

 same depth, where gravity is approximately cancelled out by free surface and bottom. 



