959 
dg = 
il & 
(II-33) 
= 
This equation is then integrated numerically by use of Gregory's formula (see e.g. 
the Mathematics of Physics and Chemistry by Margenau and Murphy, D. van Nostrand Co. 
1943, p. 459) from 
-0.00212286 
1.3435 - 0.0173284 - (1.25124) 
=t=Ds 
x=ltox= = 0.92429 
IR! 
(for the point) for several values of Y greater than 
@, min 
IRI 
The results of these integrations are given in Table IX. 
Table IX fopiis of Thiegotio tee ¢ ase Cansaien of. 
Value of fg as Obtained in Calculation for Pay is 
0.1835. 
0,4078 Radi Point a: 6). 
¢ 
We (radians) 
0.184 0.3813 
2195 23671 
2230 23528 
The data in this table indicate that there is no value of } that will give a 
value of ¢ as great as ¢,. Thus, it is assumed that the ray of light considered 
for this point has gone ough the point of total refleetion after leaving the 
diffuse source of light, the lucite grid. For each of the three values of - 
then, the value of r,43, was calculated (Eq. (II-18)), amd the numerical iptegration 
of Eq. (II-33) was carried out in two steps, first, from x = 1 up to x = EXE 
and then up to x-= 0.92429. The results of these integrations beyond the 
point of total reflection are given as a function of prin Table X. 
Table X Results of Integration for 9 Beyond Point of Tot eflection. 
Value of fg as Obtained in Calculation for p,,, is 0.4078 
ii i = 
am t 
_(radians)_ 
0.184 0.3907 
0195 4061 
«230 04232 
A plot of these results is given in Fig. 135, from which the value of ¥ to give 
a § = gg = 0.4078 radian is found to be 0.197. 
Since the value of (R{ for this shot, Film 536, was 15.97 in., Op is obtained 
as 0.197 x 15.97 = 3.15 in. : 
To convert this to a value of 04, use is made of Ea. (II-24), where c is taken 
as 0.0645 in, [lass ot is taken as 1.23, IRI is taken as 15.97 
in., and r is the value of r' - Dy for Point 22, Film 536 (=0.92429 x 15.97 = 14.76 
in.). This leads to a value of %& = 39.1 Msec. 
78 15518 
