of Edinburgh^ Session 1865 - 66 . 497 
case in deep-sea cable laying, he made no farther reference to the 
general problem in the present address. 
When a cable is laid at uniform speed, on a level bottom, quite 
straight, but without tension, it forms an inclined straight line, 
from the point where it enters the water, to the bottom, and each 
point of it clearly moves uniformly in a straight line towards the 
position on the bottom that it ultimately occupies.* That is to 
say, each particle of the cable moves uniformly along the base of 
an isosceles triangle, of which the two equal sides are the inclined 
portion of the cable between it and the bottom, and the line along 
the bottom which this portion of the cable covers when laid. When 
the cable is paid out from the ship at a rate exceeding that of the 
ship’s progress, the velocity and direction of the motion of any 
particle of it through the water are to be found by compounding 
a velocity along the inclined side, equal to this excess, with the 
velocity already determined, along the base of the isosceles triangle. 
The angle between the equal sides of the isosceles triangle, 
that is to say, the inclination which the cable takes in the water, 
is determined by the condition, that the transverse component of 
the cable’s weight in water is equal to the transverse component of 
the resistance of the water to its motion. Its tension where it 
enters the water is equal to the longitudinal component of the 
weight (or, which is the same, the whole weight of a length of 
cable hanging vertically down to the bottom), diminished by 
the longitudinal component of the fluid resistance. In the laying 
of the Atlantic cable, when the depth was two miles, the rate of 
the ship six miles an hour, and the rate of paying out of the cable 
seven miles an hour, the resistance to the egress of the cable, 
accurately measured by a dynamometer, was only 14 cwt. But it 
must have been as much as 28 cwt., or the weight of two miles of 
the cable hanging vertically down in water, were it not for the fric- 
tional resistance of the water against the cable slipping, as it were, 
down an inclined plane from the ship to the bottom, which therefore 
must have borne the difference, or 14 cwt. Accurate observations 
are wanting as to the angle at which the cable entered the water ; 
but from measurements of angles at the stern of the ship, and a 
* Precisely the movement of a battalion in line changing front. 
