37G 
MR. GEORGE W. WALKER ON 
thus 
The resultant horizontal movement along OX is H, where 
H = — (A + A 2 ) cos e + A 3 sin e', 
rr j i _ _ 2/u 2 sin e sin 2e ' 
{sin 2e sin 2 e' + /u 2 cos 2 2e'} 
The resultant vertical movement along OZ is V, where 
V = — (A — A 2 ) sin e + A 3 cos e' 
thus 
V/A = — 
2 /u 2 sin e cos 2e' 
{sin 2e sin 2e' + /u 2 cos 2 2e'| 
The apparent angle of emergence e is given by 
tan e = Y/H = — cot 2e\ 
and hence 
sin e = 1 — 2/u -2 cos 2 e, 
a relation obtained by Wiechert. 
Table I.—Longitudinal Disturbance Incident, 
/x = 1788, fx cos e' = cos e. 
• 
e. 
e. 
A s /A. 
a 3 /a. 
H/A. 
Y/A. 
o 
0 
56 
0 
- 1-0000 
-o-oooo 
-0-0000 
-0-0000 
5 
56 
8 
0-4814 
0-3797 
0-8322 
0-3407 
10 
56 
35 
0-2229 
0-5946 
1-2592 
0-5398 
15 
57 
18 
0-0985 
0-7380 
1-4918 
0-6830 
20 
58 
18 
0-0544 
0-8466 
1-6084 
0-8054 
25 
59 
33 
0-0609 
0-9346 
1-6563 
0-9219 
30 
61 
2 . 
0-1023 
1-0039 
1-6570 
1-0381 
35 
62 
44 
0-1689 
1-0587 
1-6219 
1-1555 
40 
64 
38 
0-2537 
1-0909 
1-5574 
1-2732 
45 
66 
42 
0-3501 
1-0989 
1-4692 
1-3894 
50 
68 
56 
0-4537 
1-0797 
1-3585 
1-5016 
55 
71 
17 
0-5584 
1-0315 
1•2307 
1-6077 
60 
73 
46 
0-6607 
0-9534 
1-0846 
1-7047 
65 
76 
20 
0-7553 
0-8465 
0-9256 
1-7908 
70 
78 
58 
0-8383 
0-7131 
0-7556 
1-8640 
75 
81 
41 
0-9070 
0-5566 
0-5743 
1-9225 
80 
84 
26 
0-9580 
0-3817 
0-3867 
1-9651 
85 
87 
12 
0-9894 
0-1941 
0-1952 
1-9913 
90 
90 
0 
1-0000 
0-0000 
0-0000 
2-0000 
In general A 2 vanishes for two values of e, and in the particular case /x 2 = 3, which 
holds for an ideal material with Poisson’s ratio = the values at which A 2 vanishes 
are e = 12° 47' and e = 30°. 
