MOTION OF A POINT 



FIG. 1 



paper itself supplies a second frame of reference. Suppose that 

 the moving point starts at A, and that during the motion that 

 point of the first frame of reference which originally coincided 

 with the moving point has moved 

 from A to B, while the point itself 

 has moved to C. Then the line AB 

 represents the motion of frame 1 

 relative to frame 2, while BC repre- --'"' 

 sents the motion of the moving point 

 relative to frame 1. The whole mo- 

 tion of the point relative to frame 2 is represented by AC. The 

 motion AC is said to be compounded of the two motions AB, BC, 

 or is said to be the resultant of the two motions. Thus : 



If a point moves a distance BC relatively to frame 1, while 

 frame 1 moves a distance AB relatively to frame 2, the resultant 

 motion of the point relative to frame 2 will ~be the distance AC, 

 obtained by taking the two distances AB, BC and placing them in 

 position in such a way that the point B at which the one ends is 

 also the point at which the other begins. 



There is a second way of compounding two motions. Let x, y 

 represent the two motions. The rule already obtained directs us to 

 construct a triangle ABC, to have x, y for the sides AB, BC, and 

 then AC will be the motion required. Having constructed such a 



triangle ABC, let us 

 D O complete the paral- 

 lelogram ABCD by 

 drawing AD, CD 

 parallel to the side 

 of the triangle. 

 Then AD, being 



equal to BC, will also represent the motion y, so that we may say 

 that the two edges of the parallelogram which meet in A represent 

 the two motions to be compounded, while the diagonal A C through 

 A has already been, seen to represent the resultant motion. Thus 

 we have the following rule for compounding two motions x, y : 



