1904-5.] Lord Kelvin on Deep Sea Ship- Waves. 
1083 
have seen, a maximum for values of — if/ from 0 to 35° 16', and 
a minimum for values from this to 90°, we see that the proper 
suffix in columns 4, 6, for the first four lines of each column is 1, 
and for the last six lines is 2. 
Col. 1. 
Col. 2. 
Col. 3. 
Col. 4. 
Col. 5. 
Col. 6. 
-rP 
X 
a 
y 
a 
u 
r d 2 u 
a d\f/ 2 
fa sec 2 if/ 
V A ’ £ 
0° 
1-0000 
o-oooo 
1-00000 
1-00000 
1-0000 
10° 
1-0145 
•1685 
•97239 
•93782 
1-0647 
20° 
1*0497 
•3201 
•91587 
•73497 
1-3210 
30° 
1 -0825 
•3750 
•87290 
•33333 
2-3094 
35° 16' 
1-0887 
•3849 
•86602 
o-ooooo 
OO 
40° 
1-0826 
•3773 
•87225 
- -40830 
2-6660 
50° 
1-0201 
•3166 
•93624 
- 1-84070 
1-7839 
60° 
•8750 
•2165 
1-10941 
- 5-00003 
1-7888 
70° 
•6441 
•1100 
1-53041 
-14-0987 
2-2793 
80° 
•3421 
•0297 
2-91222 
-63-3341 
4-1672 
90° 
o-oooo 
0 0000 
OO 
— OO 
OO 
§94. In (130), k is generally a function of if/; hut if the 
forcive is circular, (§ 81 above) A is a constant, and for 
points on one of the isophasal curves (a = constant) the only 
variable coefficients of the sine are sec 2 if/, and /3~ l . But for 
different isophasal curves the coefficient in (130) expressing the 
magnitude of the range above and below mean level, varies 
inversely as Ja. For mid-wake (if/ = 0) a is simply the distance 
from the forcive : and we conclude, not merely for our point- 
forcive, but for a great ship, that the waves at a very large 
number of wave-lengths right astern, are smaller in height 
inversely as the square root of the distance from the forcive or 
from the middle of the ship. 
§ 95. The infinity for if/ — ± 35° 16' represents a feature 
analogous to a caustic in optics. There is in nature no infinity 
for either case, if the source is finite and distributed, not infin- 
itely intense and confined to an infinitely small space. According 
to the methods followed in §§ 1-72 above, we have in every 
case a finite intensity of source, or of forcive, except in § 80 
where we have supposed b infinitely small, in comparison with A, 
we avoid the infinity shown in column 6 : and can, by great 
labour, calculate a table of mitigated numbers, rising to a very 
