OF CENTRAL FORCES. 27 



towards the right hand B C, moving all the while in the LECT. 

 diagonal line L; and will be found at g when the sliding >^^s~^ 

 part is drawn out as far as it was before; which then 

 will have caused the thread to draw up the ball to the 

 top of the inside of the square, just as high as it was 

 before, when drawn up singly by the thread without 

 moving the sliding part. 



If the acting forces are equal, but at oblique angles 

 to each other, so will the sides of the parallelogram be : 

 and the diagonal run through by the moving body will 

 be longer or shorter, according as the obliquity is great- 

 er or smaller. Thus, if two equal forces act conjointly 

 upon a ball or any other body, 

 one having a tendency to move 

 it towards B in the same time 

 that the other has a tendency to 

 1$ move through an equal space to- 



wards D ; it will describe a diagonal line in the same 

 time that either of the single forces would have caused 

 it to describe either of the sides. If one of the forces 

 be greater than the other, then one side of the parallelo- 

 gram will be so much longer than the other. For, if 

 one force singly would carry the body through the 

 space towards , in the same time that the other would 

 have carried it through the space towards D, the joint 

 action of both will carry it in the same time through the 

 space to F, which is the diagonal of the oblique pa- 

 rallelogram. 



If both forces act upon the body in such a manner, 

 as to move it uniformly, the diagonal described will be 

 a straight line ; but if one of the forces acts in such a 

 manner as to make the body move faster and faster, then 

 the line described will be a curve. And this is the case 

 of all bodies which are projected in rectilineal direc- 

 tions, and at the same time acted upon by the power of 

 gravity ; which has a constant tendency to accelerate 

 their motions in the direction wherein it acts. 



