294 
SiS 
Thus the thickness works out at about 1075 cm. The calculation is practically 
meaningless, except in so far as It shows that the pulse thickness is less than the smallest 
thickness for which the calculation would be a reasonable representation of the facts. 
The step-by-step calculations. 
A modification of the method described in Report °A" was used. 
The first eight steps were performed in exactly the same way as described in Report "A*. 
The course of the disturbance was followed by means of local distortions and displacements of an 
outward moving curve P and an Inward moving curve Q, {na sma)) Interval T 
oP = @ = —- 2ucT/r. 
Unfortunately, the values of T needed to follow the disturbance to 6 charge radli in about 
30 steps require val;es of 7 rather too large for tne second order corrections to P and Q to be 
inappreciable, We therefore modified the procedure after 8 very small steps to 
ap = — 2 (uct/r), 
dQ 
" 
- 2 (uct/r) 9 
where the average values were found by a two forward one backward scheme. 
Suppose that the steps up to (n - 1) are complete, and have been accepted as correct. 
The nth and the (n+ 1)th steps are then made by the Report "A" procedure. From the (n+ 1) 
values, the dP values In the nth step are corrected, by taking the average of 2uct/r in the nth 
step and 2ucr/r in the (n + 1)th step, the values in the latter case belng found at the points 
to which the ° curve had moved. Similarly, the dQ values are corrected. From the adjusted 
nth step, adjustments were then made in the (n+ 1) step, and the (n + 2) step done by Report "A°. 
A step backwards from (n + 2) to (n + 1) then gave the corrected (n+ 1)th step. Then (n + 2) 
was corrected, and (n + 3) begun. Thus every step was in fact performed three times, being 
averaged from information provided from steps on either side. it Is much quicker to make the 
corrections than it would De to take 7 one third as small, and perform three steps, because many 
of the columns do not change, and only one sheet of jraph paper Is needed for the three phases 
of one step. 
Results. 
The results of the calculations are shown in Figures 3, 4, 5, 6 and 7. Figures 3, 4 
and 5 have been given in a form that applies to a 1800 1b. charge; simple scale changes by the 
cube root law would give the corresponding curves for any other welght of charge. The oressure 
and velocity distributions in the inner regions of the bubble are not shown because the calculated 
values are not rellable. All that can be said is that In the later stages of the calculations, 
the pressure in the bubble was rapidly tending towards uniformity, and that the gas radial velocity 
did not anywhere exceed aDout 200-300 m./ second. 
The calculated shock wave pressure In tons/square Inch at x charge radi! over the range 
1<x <8 fits closely to the law 
. = 46 ,2/x 
x 
Thus P at D feet froma charge W 1b. should be 
1/3 
ps Sans exp { 0.270 w/3p } 
The pressure at 50 feet from a 300 1b, charge Is calculated to be 1940 1b./square Inch, 
compared with the experimental value 2100 1b./square Inch. (Report °B*), 
The asymptotic formula for P as D~& Is 
1/3 
Po o= 144000 W'' gD 1b./square Inch, 
Compared with the experimental formula (Wood) 
> = 120 W%*38%p 1b, /square tach 
Correcting seve. 
