CHAPTER XIL
PARALLELOGRAM OF FORCES

THIS is a graphical method of representing the resultant of two
forces acting on a point and the method is applied to such questions in
navigation and seamanship as may lend themselves to demonstration
in this branch of mechanics

The proposition is stated as follows,—If two forces acting at a
point be represented in magnitude and direction by the two adjacent
sides of a parallelogram drawn from the point and the parallelogram
be completed, then the diagonal drawn from the point of application
represents the resultant force in magnitude and direction.

A Canal Boat.—A canal boat is towed from the bank by a rope AR,
This pull is resolved into a fore-and-aft component AP propelling the

boat ahead, and an athwartship pull AQ
> which draws her into the bank, but this is
counteracted by the man who is steering
* ° when he pushes the helm, or tiller, two

FlS- ** names for the same lever, a little to the

starboard side of the boat, thus causing the blade of the rudder to
incline to port and to keep the boat's head off the bank.

Current Sailing.—The triangle of forces also comes
into current sailing, as demonstrated by the following
example. A ship is steaming South at 12 knots with
a current setting W.S W. at 4 knots. Find the course
made good by the ship and her effective speed.

Construction.—With a protractor and a scale of
equal parts, draw AB, South 12 miles, and BO,
W.S.W. 4 miles. Join AC. Tten AC is the direction
the ship would travel over the ground and the length
of AC is the distance she would cover in one hour.

The parallelogram may be completed by drawing
AD parallel to BC, and DC parallel to AB.

Tie course made good is along AC, S. 16}° W.,
and her effective speed is the length of AC, 13^ miles

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