283 
-itie 
in order not to put tco great a strain on the accuracy of (19), we first take a 
comparatively small value of R, mamely 8 = 274, |.e, 100 cm, greater than that of the last step 
in the step-by-step calculations. The rest of the pressure-radius curve, for want of something 
better, we jet from applying tne ordinary theory of sound to the pressure-radius curve of the 
27th step, Actually the error causod by this approximation appears to be insignificant 
Having obtained the pressure-radius curve when thc shock wave is at R ® 274, we may now 
repeat the argument and get the curve at a later stayc and soon. By proceeding in three or 
four steps we finally reach a staje where the shock wave Is at R = 1665 cm. Table 5 gives our 
results for the differencc In pressure on the two sides of the shock wave as a function of the 
radius of the wave. The waits are 20? kam cm? for pressure and cm. for radius. For purposes 
of changing the units, 1 kym/cm? = 0.97 atmos. = 6.4 tons/in’. 
TABLE 5, 
We have also included u, the mass velocity at the shock wave front, the units being 
metres per second. 
Figure 4 shows a alot of PR against R. If the theory of sound were a valid approximation 
at all values of R, then PR would be constant, 
Comparison with Experiment. 
Tne results of some measurements on the pressure due to the explosion of 300 1b. of 
T.N.T. Surrounded by water are jiven in the "Compilation of data resulting from trials to 
determine the explosive effects of alrcraft bombs" (Research Department, woolwich). The 
measurements were made at a distance of 50 feet, Our figures refer to a spherical charge of 
mass 390 1D. To convert our results into a form in which they may be directly comparea with 
the experimental values we must divide our time scale by 4/ (390/306) = 1.091, and divide our 
radius scale by tnis same factor. Now 50' = 1540 cm; hence, to get the pressure and velocity 
at this distance from a 300 1b. Ccharye, all that we need is to yet tne pressure and velocity in 
our case at R = 1665 cm. From Table 5 we sec that the initial oressure, attained on the arrival 
of the shock wave, is 0.122, or 0.8 tonsf inch?. This agrees perfectly with the experimental 
results. 
Figure 5 shows tne time variation of the pressure at 50' from the 300 1b. charge, The 
experimental curve is also snown. The agreement nere is not good, but there is a rough similarity 
between the two curves. The difference may in part be due to tne experimental charge not belng 
quite spherical; this would caus2 fluctuations in the pressure-time curve to be smeared out. 
In any case, the theoretical curve does seem definitely to Jrop more rapidly than the experimental. 
As we nee already explained, it is very difficult to yet tne oressure at times later tnan about 
0.7 x 1077 seconds after the arrival of the shock wave, because the pressure then corresponds 
with the very complicated sequence of events that occur near tne centre of the charge after the 
main rarefaction wave has passed and the oressure is oscillating rapidly. 
The very yood agreement between the initial pressures yives one confidence that the 
variation of the shock wav~ or2ssure with radius Is roughly right. 
Acknowledgement. : 
The problem whose approximate solution is described In this paper was suggested to 
the writer by G.|. Taylor. 
