If the gas globe is stationary, I.e., Z- constant, then froB the expression (^) 

 for ^ 



T f £1^1 -!- '^^^ T f ' + ' 



711 



Noting that 





we obtain 



Integrating by parts, we find 



Hence the complete solution $ is given by 



The evaluation of tha integrals involved in ^ for an actual gas globe is straight 

 forward, but lengthy. It is convenient, therefore, to introduce a simplifying assumption, 

 the value of irtiich must be tested by analysis of experimental data. If the period, f 

 of the first pulsation of the gas globe is much less than the time interval after the 

 explosion, it is reasonable to suppose that 



VCt) = V , O^t^T' , 

 where the constant "S/ is some average volume for the period I . Thue 



