336 



The plane h\ wliich the plate is supported is now finite and thus 

 we use £q. (13) of Part II \\ath J^ finite ,v/hich we repeat here: 



(18) 



The deflection z^ Ct) for a parabolic profile becomes 



x,a)= -E:^^ Ci&^^-GrCtt-e,)]. (19) 



In the incompressive approximation corresponding to Eq. (16), one gets 



'- = ^ '^^''^o 6C(>), 



^u. -(*/^/ ^ 



(20) 



iVhen dj is sniall relative to © , a deflection x,^ equal to one-half that 

 of a plate supported in an infinite wall is approached, itoen 9^ is greater 

 than the time of deflection calculated by liq, (16), the result for the in- 

 finite wall is obtained, since G(6-©- ) and its derivatives vanish for 

 t-©j less than zero. 



On general grounds, we may surmise that -z.^ will approach propor- 

 tionality with the iTipulse I of the incident wave when t^ is large compared 

 with Q , while it will approach proportionality with the peak pressure j^^^ 

 when t^ is si:iall compared with © , In the incompres^^ive approximation. 



27 



