953 
the average radius vecter for the vector N. Pay Was then plotted against JR] -r 
(see Figures 108, 109, 110 and 111) on semi-log paper. Within experimental scattsr 
the points fall on a straight line which was extrapolated to |RI - r,y = 0, 
that is, to the shock front. The pressure at this point was taken to be the peak 
pressure of the shock wave. The error in the assumption as to what value of r,y the 
value of pay applies should go to zero in the limit, (RI =r,, = 0. 
(i) Tee of Measurement. Before the shot, the perpendicular distance from 
the camera lens to the grid was measured. A cross was marked on the lucite 
grid at the foot of this perpendicular, and the distance s (Figure 134) wa 
measured from the center of the charge to the cross. An additional cross 210/ 
was marked on the lucite grid on the extension of the line joining the charge 
and the first cross about 4 in. (measured accurately) beyond the first cross. 
This second cross was placed so as to be ahead of the shock wave, and thus to 
appear undistorted in the final picture. It was from this measurement from 
the charge to the second cross that the radius of the shock wave was deter- 
mined on the final photograph. The illumination was provided by a flash charge 
for which the firing was delayed by means of primacord from the firing of the 
charge which produced the shock wave to be studied. 
The measurements were taken from prints of the original photograph. With a 
scale factor for the print determined from the undistorted part of the grid, 
the charge position was determined from the experimental measurements refer- 
red to the crosses marked on the grid. By use of this as a center, the shock 
front was drawn in on the print as a circle whose radius was such that it 
passed through the breaks in the lines of the undistorted and distorted parts 
of the grid. Several of the undistorted lines were extended behind the shock 
ont giving intersections which are called "actual" intersections to which 
correspond the "apparent" intersections seen behind the shock. There was no 
difficulty in assigning any given actual intersection to an apparent inter- 
section. Through each pair of intersections a radial line was drawn from the 
charge position, and was extended to intersect the shock front. This is the 
intercept of the optical plane in the plane of the grid. The distances r’ 
and Dy (Figure 134) can be measured directly on this line. R , the radius 
of the shock front, was obtained on the print by reference to the crosses 
marked on the lucite grid. The distance d is obtained by measuring the 
perpendicular distance from the cross to the intercept line and using this 
measurement together with the experimental measurement of the distance from 
the camera lens to the lucite grid. 
(b) culatio: ocedure for Time Constan onent: Decay Constant with Dis C) 
eh: ont). The path of a ray of light in a non-homogeneous medium has been 
treated very thoroughly by Richard Gans (see e.g. Handbuch der rimental 
Physik, Volume 19, p. 341 ff. and Ann d Physik (4), 47, 709 (1915) ). From his 
derivation based on Snell's law (see reference to Handbuch der Experimental Physik) 
for a medium in which the index of refraction is a function only of r, the radius 
in plane polar coordinates, the following differential equation is obtained for the 
path of a ray of light: 
Dp IRI sin i, dr 
dg = ’ (II-13) 
r ex - Dy” IRV sin® is 
where ¢ is the polar angle, (Rl is the radius of the shock front, r is the length 
of the radius vector to any point on the path, i, is the angle made by the ray of 
light and the radius vector to the point, r= (Ri , 6 = 0 (see Fig. 134). ¢ is 
measured clockwise from the point of entry into the shock wave of the reverse 
vector HM (Fig. 134) for the ray of light studied. In Fig. 134 Sg, the polar angle 
at the grid, is shown. Dy is the index of refraction at r = |RI, and n is the 
index of refraction at r. 
10/ The second cross is not necessary if the position of the first cross is corrected for 
optical distortion. 
T2 15518 
