(a) 
957 
, (II-30) 
and thus, 
=i ee (II-31) 
[RI 
This latter treatment is a more direct approach, but in neither case is the 
variation of 0, with IR] stated. This is not an important factor however, Eqs. 
(II-24) and (II-31) are very nearly equivalent numerically, and in the applications 
Eq. (II-24) will be used. 
Possible Errors. The most apparent source of error in this method of measuring 
peak pressure and time constant is the possibility of mechanical distortion of 
the lucite grid by the impact of the shock wave. Preliminary measurements on the 
velocity of sound in lucite indicate a value of approximately 6.0 ft./msec. Thus 
the shock wave started at the center of the edge of the lucite grid travels faster 
in the lucite than the shock wave in the water, and the possibility for mechanical 
distortion of the lucite grid at the time of the photograph is increased. 
Measurements on the photographs of the two shots reported in Sec. III, 3, a 
indicate that such mechanical distortion as well as lens distortion is very small, 
however. If the grid lines ahead of the shock are extended far behind the shock 
front, they coincide within drawing errors, with the apparent position of the grid 
lines in this region of "zero" optical distortion. Since the "direction" of the 
displacement due to optical distortion is the same as that due to mechanical 
distortion, that is, away from the charge, this result indicates a very small 
mechanical distortion. Also the fact that the edge of the lucite grid tovards the 
charge appears as a straight line in the shot photographs indicates no mechanical 
distortion of the lucite grid in the interval between the time of impact of the 
edge of the grid and the time of the photograph. It should be mentioned that the 
curved contour at the left of the grid photograph (Fig. 107) is not the edge of 
the grid, but rather the edge of a paper diffusion screen behind the grid. The edge 
of the grid is the line in which the diagonal grid lines terminate. Although there 
may be some slight curvature to this line in the photograph published, the line on 
the original print from which this print was made is as close to a straight line as 
is measurable. Thus mechanical or lens distortion is felt to have little effect on 
the results obtained by the optical-distortion method. 
Another source of error is in using the index of refraction-pressure coefficient 
measured in fresh water for the studies of pressure and time constant in salt water. 
Preliminary calculations based on the assumption that the difference in the index of 
refraction between fresh and salt water at high pressure is the same as it would be 
at zero pressure but at the concentration of salt per unit volume that the water 
would have at the high pressure have been made. These calculations indicate that 
the error involved in the assumption that the index of refraction-pressure coefficient 
is independent of the salinity is of the order of 2.5%. The direction of this error 
is such as to make the calculated pressure too great. The data necessary for these 
calculations on the effect of salinity are from a report by E. A. Brodsky and J. M. 
Scherschewer (Z. Phys. Chem., B, 23, 412 (1933)). 
= 
The possibility of error in the assumption that Snell's Law of Refraction holds 
in a non-homogeneous medium also deserves some consideration. Gans (Ann. d. Phys. 
(4), 47, 709 (1915)) studies in detail the case of refraction of a linearly-polarized 
light wave in a non-homogeneous medium by use of the electromagnetic-field equations. 
He assumes that n = Ve » Where n is the index of refraction of the medium and € 
ig the dielectric constant. This relation, of course, does not hold for water. He 
shows that under these assumptions Snell's Law holds over most of the light path, but 
very near the point of total reflection the ray of light deviates from the path 
predicted by Snell's Law and undergoes an angular discontinuity, "knick", at the 
point of total reflection. A short distance beyond the point of total reflection, 
the path again coincides with the path predicted by Snell's Law. 
1% 15518 
