222 PHOTOGRAPHY OF UNDERWATER EXPLOSIONS 



have not been accounted for. It seems unlikely that the piezoelectric 

 gauge data are ten-fifteen per cent in error, in view of their much better 

 agreement with results from ball-crusher gauges, dome velocity calcu- 

 lations, and independent calibrations and measurements. The more 

 likely possibility is therefore the one of inaccuracies in the method. 

 Shock distortion of the screen by the pressure wave was found, by 

 measurements on the records, to be small. Another source of error is 

 uncertainty as to the refractive index-pressure relation for the salt 

 water used in the experimental arrangement. No direct figures for 

 salt water were available, and the relation employed was based on 

 isothermal values at high pressures corrected to adiabatic conditions 

 from data at lower pressures. Further uncertainties exist because of a 

 necessary wavelength correction and possible temperature effects in 

 second order terms. There are reasons to believe that none of these 

 uncertainties has a large effect on the relation actually used, but either 

 a direct determination for salt water or repetition of the explosion 

 measurement in fresh water would be desirable. 



Halverson has also extended the refraction measurement to determi- 

 nations of the decay constant of the pressure wave with distance behind 

 the shock front, the profile being assumed exponential in form. This 

 determination evidently requires an examination of the actual path be- 

 hind the shock front. Assuming that Snell's law applies, i.e., that the 

 ray is described by geometrical optics, the differential equation of the 

 path can be integrated numerically for any assumed value of decay 

 constant 6{r) in the expression P{r) = P^(i^)e~(^-'')/^W where R is the 

 shock front radius. This calculation is repeated for several possible 

 values of d(r) to find by interpolation the one consistent with the ob- 

 served displacement of a coordinate intersection behind the shock front. 

 The decay constant so obtained is of course for spatial variation, and a 

 conversion must take into account the variation with R of peak pressure 

 Pm, and strictly should include variation of d{r) with R. The latter 

 effect of spreading is unimportant, however, and can be neglected. 



The calculations outlined have been carried out for the shots pre- 

 viously mentioned and gave an average time constant of 40.4 /xsec. 

 for 5 points behind the front, the average deviation from the mean be- 

 ing dbl.7 jLisec. with no indication of systematic variation for different 

 points. The initial time constant of deca}^ from piezoelectric data is 

 50 )usec. or about 20 per cent higher. 



The measurement of scale distortions described in the foregoing is 

 open to the basic objection that the results obtained are not purely 

 analytic deductions from basic principles, but depend in part on assump- 

 tions as to the form of the refraction gradient. It can readily be shown 

 that this is an essential limitation of the method, as there are finite 

 regions near ^discontinuities which any possible ray must completely 



