Page:The Kinematics of Machinery.djvu/81

 determined by distances measured from any two points in the section of the frame traversed by that plane.

Prop. III. The motion of a plane figure relatively to a plane in which it moves is known if the motions of any two of its points P and Q (Fig. 15) relatively to two fixed points A and B in the plane of motion be given. For when the positions of P and Q are known, the positions of every other point in the moving figure

Fir*. 14.

can be found by considering it as the vertex of a triangle of which the position of the base and the lengths of all three sides are known. The motion of any plane figure may. there- fore be expressed by that of any line in it. The motion of the line P Q relatively to the line A B is therefore the same as that of the figure PQ to the figure A B.

. 15.

Example. In order to determine the motion of a plane equatorial section of any planet relatively to the plane of the solar system (assum- ing the section to move in that plane), the motions of at least two points in that section relatively to the plane of motion must be known. Visible inequalities on the surface of a star, or a spot on the sun, may be supposed to furnish, points relatively to which the motion of the section can be observed.