Principle of Virtual Velocities, 77 



Art, YI. — Oti the Principle of Virtual Velocities ; by Prof. 

 Theodore Strong.* 



We shall premise the following definitions and principles. 



Def. I. Whatever moves or tends to move any portion of mat- 

 ter, is called force ; and the point at which the force is applied is 

 called its point of application. 



Def 2. Our idea of force requires us to cohsider its action as 

 being in a right line which passes through its point of application ; 

 this line is called the line of the force's action ; and by the direc- 

 tion of the force we mean the direction of that part of this line 

 (reckoned from the point of application) into which the force 

 moves or tends to move the body to which it is applied. 



If we represent any given (or assumed) force by unity, then if 

 any other forces contain the unit of force P, d, (fcc. times, these 

 forces will be expressed (by the numbers) P, Q., &c. If a body 

 is acted on by two forces in the same direction, their resultant is 

 expressed by their sum, and acts in the same direction as the 

 forces ; but if the forces act in opposite directions, the resultant 

 will equal the diiference of the forces, and acts in the direction 

 of the greater force. 



Investigation of the principle. — Let a body or a system of 

 bodies (or material points) be affected by the forces P, Q, R, &c. 

 in such a manner as to be in equilibrium. Imagine points re- 

 garded as fixed to be taken in the lines in which the forces act, 

 such that the forces shall at the same time each tend to increase 

 or decrease the distance of its point of application from the point 

 taken in the line of its action, (the positions of the points in other 

 respects being arbitrary ;) we shall call the fixed point which is 

 taken in the line of action of any force (for simplicity) the centre 

 of that force. 



Let p, q, r, &c. denote the distances of the points of application 

 of P, Gi, R, (fee. from their respective centres ; then if we denote 

 the sum of the products Pp, Giq, (fee. (which are each evidently 



* Prof. SiLLiMAN — Dear Sir : As some objections have been made to the first 

 part of my paper on Virtual Velocities, (see this Journal, Vol. xLii, p. 66,) I have 

 concluded to re-write the part which has been objected to, and to enter more fully 

 into detail in several respects than in that article, for the purpose of clearness and 

 explanation. Yours, &c. T. Strong. 



JVew Brunswick, Jan. 25, 1842. 



