246 Dr. Stevelly on the Composition of Forces. 



I. Two equal and directly opposite forces which act simulta- 

 neously on a material particle must manifestly each counteract any 

 tendency to change its place given to the particle by the other; 

 that is, they are in cequilibrio ; and an absurd conclusion can be 

 readily shown to follow from supposing any two forces acting 

 together at a material point to be in cequilibrio but such as are 

 both equal and directly opposed. 



(a) Hence any number of forces which act simultaneously on 

 a material point must have a single force, called their resultant, 

 which, acting alone on that point, would produce in it the same 

 tendency to move which they do acting together ; for, however 

 numerous and varied they may be, they can give to that point a 

 tendency to move in only some one direction and with some de- 

 finite energy. A single force, therefore, equal in energy to that 

 and opposite in direction, might be assigned which would equili- 

 brate against them all, and the single force equal and directly 

 opposite to this would obviously have the same effect as all of 

 them together. 



Definition. Forces are represented by straight lines drawn 

 either in the very direction in which they act, or along parallel 

 lines in the direction along which they solicit the material point 

 on which they act, lengths being taken along those representa- 

 tive lines which contain as many linear units and decimal parts 

 of a unit as the force to be represented contains units of force 

 and decimal parts of such a unit. 



(b) Hence also it becomes obvious that if two forces which act 

 together on a material point, say P and Q, have a resultant, say 

 R, acting in a known direction in relation to the directions in 

 which P and Q act, if instead of P and Q we apply to the same 

 point two forces each equal to P and Q in magnitude respect- 

 ively, but each directly opposite in direction to the one it replaces, 

 the resultant of this latter pair is equal to E- in magnitude, but 

 exactly opposite to it in direction. 



(c) Hence also it is easy to show that the representative of 

 the resultant of a number of forces which all urge a material 

 point to move in the same direction along the same right line is 

 the sum of the lines which would represent each of them sepa- 

 rately, measured in the same direction along the same line ; and 

 that the line which would represent the resultant of two forces 

 which act on the same point in opposite directions is the differ- 

 ence of the two lines which would represent each separately, mea- 

 sured in the direction of the greater force ; and hence also the 

 representative of two groups in opposite directions is the alge- 

 braic sum in the direction of the greater group. 



II. The ratio of two component forces which act together on 

 a material point determines the direction of their resultant in 



