509 
of Edinburgh, Session 1865 - 66 . 
These formulee apply to every case of uniform towing of a rope 
under water, or hauling in, or paying out, whether the lower end 
reaches the bottom or not, provided always the lower end is free 
from tension; but if it is not on the bottom, D must must denote 
its vertical depth at any moment, instead of the whole depth of the 
sea. To apply to the case of merely towing, we must put w = 0 ; or, 
to apply to hauling in, we must suppose u negative. 
It is to be remarked that the inclination assumed by the cable 
under water does not depend on its longitudinal slip through the 
water (since we assume this not to influence the transverse com- 
ponent of fluid friction), and that, according to equation (4), it is 
simply determined by the ratio of the ship’s speed to the transverse 
“ settling velocity” of the cable. 
The following table shows the ratio of the ship’s speed to the 
“ transverse settling velocity” of the cable for various degrees of 
inclination of the cable to the horizon : — 
Inclination 
of Cable 
to Horizon. 
i 
5 ° 
angle ) 
whose sine ( 
■ 6° 
is C 
8^ ) 
10 
15 
20 
25 
30 
35 
40 
Ratio of Ship’s Speed 
to “ transverse set- 
tling velocity ” 
of Cable. 
^ _\/ cos i 
p sin i 
11-4518 
8-4784 
5-7149 
3-7973 
2-8343 
2-2013 
1-8612 
1*5779 
1-3616 
Inclination 
of Cable 
to Horizon. 
45“ 
50 
51" 50' 
55 
60 
65 
70 
75 
80 
85 
Ratio of Ship’s Speed 
to “ transverse set- 
tling velocity" 
of Cable. 
-= V cost 
P sin i 
1-1892 
1-0466 
1-0000 
-9232 
•8165 
•7173 
•6224 
•5267 
•4231 
•0875 
If the inclination of the cable had been exactly 6° 45' when the 
speed of the Great Eastern was exactly 6J miles per hour, the value 
of p for the Atlantic cable of 1865 would be exactly 6J^ 8 478, or 
*765 of a mile per hour. 
