1903-4.] Lord Kelvin on Tivo-dimensional Waves. 
193 
9 /W2 \ T± 2 
h=l ; y = 4; t = 5; - £ = J- sin ( %■ + 0 ) e p 2 . 
P \p 2 ) 
Col. 1. 
Col. 2. 
Col. 3. 
Col. 4. 
Col. 5. 
Col. 6. 
1 Col. 7. 
X. 
a/-. 
P 
! 
1! 
i r-l 1 
+ <3- 
QJ 
! \ 
Initial Elevation 
of Water-surface 
at Distance x. 
sin 6. 
P 
+ 
Si i©* 
H o- 
*c n 
-f2 
e p 2 " 
Elevation of 
Water- surface at 
Time t, and 
Distance x. 
4-0 
•6965 
•7882 
•5490 
•4856 
•2298 
•07771 
4-41 
... 
0 
0 
4-5 
•6588 
•7798 
•5139 
- -0944 
•3083 
- -01917 
5-0 
•6262 
•7733 
•4843 
- ’5584 
•3823 
- -1336 
5-5 
•5981 
•7678 
•4592 
- -8457 
•4493 
- *2273 
6-0 
•5733 
•7629 
•4375 
- *9781 
•5122 
- -2872 
6-5 
•5513 
•7587 
•4185 
- -9956 
•5641 
- -3096 
7*0 
•5318 
‘7555 
•4018 
- ‘9374 
•6066 
- -3024 
7-5 
•5150 
•7522 
•3868 
- '8333 
•6462 
- -2773 
8-0 
•4980 
•7494 
•3734 
- -7053 
•6808 
- -2392 
9-0 
1 *4699 
•7451 
•3501 
- -4289 
•7372 
- -I486 
10 
•4461 
•7416 
•3308 
- *1679 
•6346 
- -04753 
10*62 
0 
0 
11 
•4255 
•7385 
•3142 
•05698 
•8147 
•01975 
12 
•4076 
•7359 
•2999 
•2428 
•8416 
•08375 
13 
•3916 
•7339 
•2874 
•3940 
•8644 
•1334 
14 
•3775 
•7318 
•2762 
•5175 
•8808 
•1721 
15 
•3648 
•7302 
•2663 
•6163 
•8954 
•2013 
16 
•3533 
•7286 
•2574 
•6953 
•9082 
•2231 
18 
•3331 
"7266 
•2419 
•8098 
•9260 
•2498 
20 
•3160 
•7256 
•2290 
•8831 
•9396 
•2622 
22 
•3014 
•7230 
•2179 
•9313 
•9497 
•2666 
24 
•2885 
•7216 
•2082 
•9627 
•9579 
•2661 
26 
•2772 
7206 
•1997 
•9815 
•9638 
•2622 
28 
•2672 
•7193 
•1923 
•9915 
•9685 
•2565 
30 
•2581 
•7187 
•1856 
•9979 
•9727 
•2505 
32 
•2500 
•7181 
•1795 
•9999 
•9759 
•2439 
34 
•2425 
•7173 
•1740 
•9993 
•9786 
•2371 
38 
•2294 
•7163 
*1643 
•9933 
•9828 
•2240 
42 
*2182 
•7155 
•1561 
•9840 
*9847 
*2188 
46 
•2084 
•7147 
*1490 
•9734 
•9883 
•2005 
50 
•2000 
•7141 
•1429 
•9623 
•9902 
•1905 
55 
•1906 
•7135 
•1360 
•9486 
•9917 
•1794 
60 
•1826 
*7129 
•1302 
•9361 
•9931 
•1697 
70 
1690 
•7120 
•1203 
•9125 
•9949 
*1535 
80 
•1581 
•7114 
*1125 
*8931 
•9961 
•1407 
100 
*1415 
•7108 
•1005 
•8626 
•9977 
•1217 
00 
0 
•7071 
0 
•7071 
1-0000 
0 
§ 8. Look at the values shown in the previous table for the 
three factors which constitute £; — we see that the first factor 
(col. 2) decreases slowly from x = 0 to x=co ; the second factor 
(col. 5) alternates between + 1 and — 1 with increasing distances 
(semi-wave-lengths) from zero to zero as x increases. The third 
PROC. ROY. SO.C, EDIN. — VOL. XX Y. 13 
