190 Proceedings of Royal Society of Edinburgh. [: 
are shed off on the two sides, travelling away from it rightwards 
and leftwards with accelerated velocities, each remaining for ever 
convex. Thus we see the beginnings of two endless processions of 
waves travelling outwards in the two directions ; originating as 
infinitesimal wavelets shed off on the two sides of the middle line. 
Each crest and each hollow travels with increasing velocity. Each 
wave-length, from crest to crest, or from hollow to hollow, becomes 
longer and longer as it advances outwards ; all this according to 
law fully expressed in (8) of § 3 above. 
§ 7. Here is now the table of numbers promised in § 5 above ; it 
practically defines the forms and magnitudes of the two and a half 
wavelets, between x = 0 and x = 2, which the space-curve for t = 5 
(figs. 2 and 3) fails to show. 
2 /rW 2 \ Zl 2 
p 2 = a 2 + /t 2 ; h= 1; g = 4; t = 5; - £= sin + 6)e p 2 . 
Col. 1. 
Col. 2. 
| 
Col. 3. 
Col. 4. 
Col. 5. 
Col. 6. 
Col. 7. 
X . 
•vA 
p 
*3 
II 
t* 
> 
§8 . 
« £ 
5 * <D * v -° 
>EJO II 
® <? g (N 1 a . 
> 
.2 
q ai to 
M O 
+ 
$2> |<^ 
CL 
-«2 
e p2 ’ 
Elevation of 
Water-surface at 
Time t , and 
Distance x. 
-<r. 
0 
1-4142 
1-0000 
1-4142 
1 0000 
10- 10 1357 
+ 10-. 10 1963 
■05 
1-4140 
'9997 
1-4140 
•3434 
,, -1478 
» >> '0717 
•064 
0 
0 
•10 
1-410 
•9987 
1-409 
- -7541 
„ 1778 
- 10-. 10 -1891 
•15 
1-407 
•9972 
1-403 
- *8997 
,, -3066 
,, ,, *3882 
•20 
1-401 
•9952 
1-393 
- -0032 
„ -3632 
,, ,, *0016 
*202 
0 
0 
•30 
1 -384 
•9894 
1 -370 
•8997 
,, 1-094 
+ 10 -. 10 1*362 
•363 
0 
0 
•40 
1 -362 
•9820 
1-338 
- -5451 
„ 4-366 
- 10 - 10 3'243 
•60 
1-309 
•9638 
1-262 
- -2341 
,, 103-9 
„ ,, 31-84 
*632 
0 
0 
•80 
1*249 
• 9*437 
1179 
•7593 
10- 5 ’ -02396 
+ 10 5 -0227 
1-00 
1-190 
•9239 
1-099 
*8962 
„ -2958 
,, -3152 
1*25 
1-118 
•9015 
1-007 
•6831 
,, 5-793 
„ „ 4*424 
1-50 
1-053 
•8817 
*9287 
•4923 
45-63 
., „ 23-67 
1-517 
0 
0 
1-75 
•9961 
•8651 
•8616 
- -6832 
„ 212-5 
_ 10-5 144-6 
2-00 
•9456 
•8506 
•8043 
- -9997 
,, 848-2 
,, ,, 8019 
2-50 
•8612 ; 
•8243 
•7142 
- 1633 
•03180 
„ 447-3 
2-54 
0 
0 
3-00 
•7952 
•8113 
•6450 
•8296 
”•08210 
•0542 
3-50 
•7411 
•7980 
•5917 
•9473 
•1516 
•1064 
Continued on p. 193. 
