Principle of Virtual Velocities, ad 
‘Arr. VI.—On the Principle of Virtual, Tdeaiiben. io Prof, 
THeopore Srrone.* 
We shall premise the following definitions and principles. 
‘Def. 1. Whatever moves or tends to move any portion of mat- 
ter, is ; called force ; and the point at which the force is applied it is 
called its point of Sioleaton: 
. Our idea of force requires us to consider its action as 
vets’ in a right line which passes throngh its point of application ; 4 
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, Q, &c. 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 equial the difference 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 ints re- 
garded as fixed to be taken in the lines in which the fo rees act, 
stich that the forces shall at the same time each tend to 
* or decrease the ¢ distance of its point of a 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 sim simplicity ) the centre 
of that force. 
‘Let p, 9, 7, &c. denote the distances of the points of application 
of P, Q, R, &c. from their respective centres; then if we denote 
the sum of the products Pp, Qq, &c. (whieh are each evidently 
* Prof. Srtumean—Dear Sir’: As some objections have been made to the first 
: part of my paper on Virtual Velocities, (see this Journal, Vol. xin, p. 66,) I 
| concluded to re-write the part which has been objected to, and to enter more fully 
into detail i in several respec ts th an in that article, for the purpose of clearness and 
erate Yours, ‘Se. T. Strona. 
