UDUCTION OP A SYSTEM OP POM9B. 



fore from equation (8) of Art 98 



-*{(*-*)+ (*-/)+(/-.?) 



./*+ Jter+jrary 



"I . I 



mains constant for all points in the plane (I) 

 (A-*T+ (*-y')' + (/-*? is constant; th 



.ire at a constant distance from the 

 central axis. FVotn thi* an.l Art. 98 it follows, that if a right 



be described :he central axis, the prin 



moment hoe the earns value for any point on the surfot* of this 



ressions which compose G in equation 

 (jO of Art 96, the latter, by Art 94, is the resolved pa 



resolved part of G' perpendicular to the dirrcti. Call 



the former part Q, and * the angle whi 



axis of (/" makes with that of R; then ain^-- , and this 



is constant so long as (/' is, that is. for every point on the 

 surface of the cylinder in the preceding Arti 



98. Th- ]>r.>|x ..iti..ns already given in this Chapter admit 



modes of demonstration, which we proceed t 

 die. 



To shew that any system of forces con always be reduced 

 force and a couple, the axis of the latter bevy pcwiOel 



to the direction of the former. 



Th- i rces can be always reduced to a force R and a couple 

 G, an i : <f> between the former and the axis of the 



cos</>- 



Resolve the couple G into two others ; one having its axis 

 parallel to the direction of R and its moment equal to O cot \ 



:ln r having its axis perpendicular to the diirction 

 and its moment equal to r/ sin *. The forces of the Utter 

 ic are therefore in a plane paralK and by pro- 



