SIX 



'' parallel to the co-,, r dii 



;d to tli- . ) - :uid '/' , 



at tin- ; . v parallel to tin- axes r68] 



will lie c'liiilibrr ly Art. 



(1), 



Filiations (1) determine A". )' . /'. It mi-lit at first a; 

 tliat ciuations (2) would determine x, y , z ; but it' we pro- 

 ceed to solve them, we find that they cannot be ri 

 true unless 



and if this condition be satisfied, and ^A', ^.Y, ^./ do i 

 vanish, then any one of the equations may be derived from 

 the other two, so that there are only two /'//// <\ nations. 



that the forces may have a single resultant the , 

 condition must be satisfied, and then any two t' equations (2) 

 will determine the locus of points at which this sinLrl result- 

 ant may be supposed to act. From the form of < fpiations (2) 

 it is obvious that this locus is a straight line, and that its 

 i'n cosines are proportional to A", 1", /. . M might 

 have been anticipated. 



In order that the force which replaces the system may pass 

 through the origin, we must have 



A = 0, 3/=0, #=0. 



83. Although a system of forces cannot alwa;. 

 to a single resultant, it can always be reduced to tiro forces. 

 For we have shewn that the system may l>e replaced by a 

 force It at the origin, and a couple G lying in a plane tin 

 the origin ; one of the forces of G may be sup] act at 



nd may be compounded with H so that this 

 resultant and the other force of '/ an < ^piivah nt to the 

 system. Since the origin is arbitrary, we see that wi. 

 system of forces is not reducible to a single force it can i 

 duced to two forces, one of which can be made to pass through 

 assigned point. 



