N= (x'-x)4+(0-y) j+(z'-z)k, (II-1) 
De=N- MW = (xt-x")it(z!-2")k 
s DyitDzk. 
The magnitude of all vectors and distances is to be taken in units of {RI , 
i.e., Ipl ‘sl. 
Consider the following cross-product relations. 
= - 
=q sin 0, 
il : (II-2) 
re =q sin @!, 
where q is a unit vector perpendicular to the plane which contains ii, Dp P, Wi and 
D and © and 6! are the angles of incidence and refraction respectively in this 
plane. This is not necessarily the plane shown in the top view in Figure 133, 
Applying Snell's Law, 
sin@® . Day 
sin 6! n Aue 
° 
where ngy is the index of refraction corresponding to the average pressure p v, 
and is the index of refraction of sea water at zero pressure, we obtain the 
relation, 
ibe ot (11-3) 
[uly : 
From the last of (Eqs. II-1) 1 
Dxp . ep - = as 
IN - i ; ae 
Dxp = ra (3 i Aut) Ikp, (11-5) 
or using (Eq. II-3), 
[NI 
which may be written, 
tit( 3-~Hhr) Goren) = 2a 
(3 
(II-5") 
l Zui = 
i‘ - _) (Yox-xoy) = Dxy, 
Ory 
1. - iM Dy + Low 
po ™ “Gy -y,2) [NT (11-5") 
949 
The distances {MI , It and £|MI can be readily obtained from the coordinates 
(xy¥5Z)y (XosYorZo)y (x',0,2"), and (x",0,2"), Although two values of the index of 
refraction can be obtained from each distortion, they are not independent, and in 
general because of the coordinates chosen and the experimental arrangment used D, 
was too small to be measured. 
Given v from the above and ny for sea water, P,. can be obtained by 
applying the relationship between the index of refra®tion and pressure for water. 
This relationship is discussed later. 
68 155 
18 
