192 



between two minimum radii should then be given quite accurately by the formu- 

 las if the Intervening maximum radius is used, whereas the interval of time 

 between two successive maxima should be the average of the periods as given 

 by the formulas for the two successive maximum radii. 



The formulas for the period have been derived from hydrodynamical 

 theory but appear to have been confirmed satisfactorily by observation. No 

 allowance has been made for the effect of the displacement of a gas globe due 

 to gravity, but this effect should be large only under extreme conditions. 



TIME-DISPLACEMENT CURVES 



A number of curves are drawn in Figure 2 which show for several am- 

 plitudes, the value of R/Rq during an oscillation as a function of the time. 

 The unit for time is the period of small oscillation, T^ ; thus the curves are 

 valid for any value of R^. They refer to the case y = 4/3, which is the eas- 

 iest to calculate. For air, however, the curves would differ so little that 

 it Is not worth while to attempt to illustrate the difference. The curves 

 were constructed by integrating Equation [32] numerically. As with the peri- 

 od, no allowance has been made for gravitational displacement of a gas globe. 



Figure 2 - Calculated Time-Displacement Curves for Undamped Oscillation 

 of a Bubble or Globe of Gas under Water 



R = radius ( = time 



R„ = radius when in equilibrium T„ = period of very small oscillations 



