378 



The reason for the discrepancy between the parabolic and tvgo-mode 

 Be ssel'-f unction theories is the artificial restraint of a parabolic profile 

 in the former. For large charges, producing shock waves of long duration, 

 the two theories give values of the maximum deflection only a few percent 

 apartj but for very small charges, producing shock waves of very short 

 duration, the results are conspicuously divergent. This situation is made 

 understandable by the fact that the two-mode Bessel- function treatment 

 gives a final pixifile vrtiich is almost parabolic for waves of long duration 

 but vrtiich is quite peaked with an abnormally raised center for waves of 

 short duration. The twD theories also give rather different times of de- 

 flection, the parabolic theory giving values of this quantity roughly 20^ 

 higher. The calculated times of deflection have not been compared with ex- 

 periment, since there j» no data yet available for noncavitating cases. 



In conclusion, the parabolic theory gives deflections which agree 

 more closely with experiment than do those given by the more elaborate tvro- 

 mode Bess el— function theory, the better agreement supposedly being due to 

 a partial cancellation of errors common to both theories by an error asso- 

 ciated with the restraint of a parabolic profile. However, the parabolic 

 theory gives results for large charges differing little from the results 

 of the more elaborate theory, and is more practical for actual computation 

 because of its greater simplicity. Where empirical pressure-time curves 

 have been used, the agreement of both theories with experiment is very good 

 in view of the nxunerous possible sources of error. 



61 



