Compound Motion. 21 



36. If two forces p and q, the directions of which are 

 right angles to each other, act at the same instant upon a body m, and 

 the force q is such as by its sole and instantaneous action to cause the 

 body to pass over AB in a determinate time, as one second, and the 

 force p is such as to cause the body to pass over AD in the same time, 

 we say that by the joint action of the two forces, q and p, the body m 

 will in the same time pass over the diagonal AE, of the parallelogram, 

 DABE, which has for its sides these same lines, AB, AD. 



Since the two forces act at the same instant upon the given 

 body, we may suppose it moving in the line AD, and that at the 

 instant of its arriving at the point A, it receives the force q in a 

 direction perpendicular to AD. Now according to article 35 

 the force q can neither increase nor diminish the velocity with 

 which it was at this moment departing from AB ; if, therefore, 

 through the point Dwe drawD.E parallel to AB, the body must 

 at the end of a second be somewhere in the line JD E, all parts of 

 which are equally distant from AB. 



The same reasoning may be adopted with regard to the 

 force q, by which it will be seen, that if through the point B, we 

 draw BE parallel to AD, the body must at the end of a second be 

 somewhere in BE. But there is only the point E which is at the 

 same time in DE and BE-, therefore at the end of a second the 

 body will be in E. 



It is also evident, that whatever course the body takes, 

 by the instantaneous action of the forces, this course must be 

 a straight line since, from the instant that the forces are ex- 

 erted, the body is abandoned to itself, and there is no cause 

 to incline it one way rather than another. Accordingly, as this 

 body passes through A and E, and without any thing to change its 

 direction, the course must be AE, that is, the diagonal of the 

 parallelogram DABE. 



We will add moreover, that the body describes AE with a 

 uniform motion, since after the joint action of the two forces, it 

 is left equally without any cause to alter its rate of moving. 1 



37. Since the two forces p and q, acting simultaneously upon 

 the body m, have no other effect than to make it describe the 1 

 diagonal AE, we infer, that instead of two forces whose directions 



