
618 Lord Kelvin on Deep-Water Two-dimensional 
The third factor (col. 6) increases gradually from e~” at 
#=0,to latw=o. At «=50h, the third factor ieee 
which is so nearly unity that the diminution of amplitude is, 
for all greater values of 2, practically given by the first factor 
alone, which diminishes from *2 at c=50h, to 0 at v=o. 
§ 9. The diagrams hitherto given, figs. 1, 2, 3, may he 
called space-curves, as on each of them abscissas represent 
distance from the centre of the disturbance. Fig. 4 is a 
time-curve (abscissas representing time) for #=2h. It 
represents a very gradual rise, from t=0 to t="6, followed 
by a fall to a minimum at t=2°8, and a succession of 
alternations, with smaller and smaller maximum elevations 
and depressions, and shorter and shorter times from zero to 
zero, on to t=. The same words with altered figures 
describe the changes of water level at any fixed position 
farther from the centre of disturbance than w=2. The 
following table shows, for the case e=100h, all the times of 
zero less than 71h, and the elevations and depressions at the 
intermediate times when the second factor (col. 5 of § 7) 
has its maximum and minimum values (+1). These 
elevations and depressions are very approximately the greatest. 
in the intervals between the zeros, because the third factor 
(col. 6, §7) varies but slowly, as shown in the first column 
of the present table. 




2 Ola ; 
h=1; »=100 ; p=100-005.h; @=tan-ta /20" =45° 18’ 
| | 
Times of Zero. Times of Zero | | 
i and of Approximate 2. andof | Approximate | 
—- Approximate) Maximum —- Approximate) Maximum | 
e*’° | Maximum |Elevationsand| ¢°° Maximum | Elevationsand | 
Elevation and) Depressions. Elevation and; Depressions. | 
_ Depression. | Depression. | 
9922 Spo Se seAds ‘T7118 50°90 . |) eam 
Hon) (eh ios | ) ae 02°42 | 0 
9616) 1980 — ‘1360 GAT3 53°90 | —*1058 
ae 23°43 0 os o'34 | 0 
OSlT (26°04 ld, easter Loiles does 56°74 | =SaOze 
ce I eZee 0 ates 58°10 | 0 
9031. | 31:04 | "1277 7023 d9°45 |  ="0993 
Cay i Cae G a 60°75 | 0 
"8750 36°54 |e rune ‘6806 62:03 | +0962 
mele) “eS'6Z | 0 Bs 63°29 0 
8480 | 4061 | 1199 6595 Ofinat — 0933 
Se) ea eke oO 0 ee 65°72 0 
8219 | 44:31 /  -+-°1162 "6392 66°90 +0904 
... | 46:04 | 0 ee 68:07 . 0: 
7904 | ARr72 — 1157 6195 | 69:21 | —'0876 
Mell eADioA 0 i TO3+ | 0 
| 


