951 
Since the computational method outlined above is somewhat lengthy, a more 
direct method, again assuming a step shock but taking advantage of the planar nature 
of the problem, was used in the actual calculations. The determination of the 
"optical plane", that containing XM, Pp, N, D, E and C, is very simple when the charge 
is in the plane of the grid, for, in this case, the intercept of the optical plane 
in the plane of the pric contains D and E. Knowing the projection of the camera on 
the line containing D and E, and the perpendicular distance d of the camera from it, 
the optical plane is determined and can be represented as in Figure 134. The 
distance IRI to which all other dimensions are referred is obtained as described 
above. r! and D, are obtained directly from the print as above, whereas d and s 
are obtained from the known position of the camera relative to the grid. To derive 
the index of refraction from the distortion of the ray M in terms of these measure- 
ments using the symbols shown in Figure 134 the following relations are used. 
tang = eee (11-6) 
where Bp may be positive or negative, and since /R/ =1, 
cos (6,8) ar! con : (II-7) 
Then using the law of cosines, 
fiul = 1+rt2-2rt cos £, (II-8) 
It can be shown, using the law of sines, that 
D 
see $ . - cos 8 aes 
On applying Snell's Law, 
= —Sin @ = @ (II-10) 
v sin © sin (0- ‘ 
Day sin 06 -1| + cos 9 pte | 
eS a a (11-11) 
n sin ®@ =- cos © tan 
re) 
where @ = 90° - (6, oa) 
In order to convert nay to pay, data on the pressure coefficients of index 
of refraction for water are required. 
Data were available for fresh water, and were assumed to hold for salt water 
as well. This assumption is felt to be valid to within a few percent as is 
indicated by some preliminary calculations. In Table VII the available data on 
the coefficients a and b in the equation, 
n(p) -n, = ap - bp? , (II-12) 
are given together with the source of the data. For the calculations of Pay 
concerning a specific point, Eq. (II-12), of course, becomes 
Day 7% = 2 Pay b Pay’ 
The type of film used in the experiments studied was Contrast Process Ortho, 
which is sensitive in a narrow range of wave length centered around ca. 4800 A.U. 
In order, then, to correct nay to pay it is necessary to obtain adiabatic values of 
a and b for a wave length of 4800 A.U. and for the proper temperature. The iso- 
thermal value of a was taken from the data Rontgen and Zehnder for a wave length 
of 5890 A.U. and the proper temperature for the given experiment. It was then 
70 15518 
