40 MEASURE OF A COUPLE. 



i.il moil. ; ir to any j r in 



M Q I IM ' ,,uple 



must remain unchanged so far as coiuvriis tin- direction of 

 the rotation which its forces woull tend to give the arm. 

 pOsin.LT it- mid. lie point fixed as in Art. 11. In other v, 

 the straight line \vhirh we have called thr . AftUTed as 



ited in that Article, must al :aain on the same 



ride of the plane of the couple. 



We may infer from Art. 11 that couples ma, 

 surcd by their moments. Let there be two eoupl. 

 which each t'oree = /', and one in which each force = (J, the 



of the couple -jual ; these couples will IK- in the 



ratio of Pto Q. For suppose, for example, that /' is to Q as 

 3 to 5; then each ot'ti. /'may be divided into ,'J equal 



forces and each of the forces Q into 5 such equal forces. Then 



uple of which each force is P may be con.-ideivd as the 

 sum of 3 equal couples of the same kind, and the couple of 

 which each force is Q as the sum of 5 such eijiml couples. 

 The effects of the couples will therefore be as 3 to , r >. Next, 

 suppose the arms of the couples urwjuul. and denote them by 

 p and q respectively. The couple which has each of its 



- = Q and its :.rm = j is equivalent to a couple hav:nu r 



each of its forces =-'^ and its arm = p, by Art. 11. The, 



couples are therefore by the first case in the ratio of P , 



that is of Pp to Qq. 



17. AYith respect to the effect of a couple, we may ob- 

 that it is shewn in works on rigid dynamics that if a < 

 act on a free rigid body it will set the body in rotation about 

 an axis passing through a certain point in the body called 

 its centre of gravity, but not necessarily perpend It -ultir tv M' 

 plane of the couple. 



48. To fnd the resultant of r of couples a 



on a body, the planes of the couples being parallel to each 

 oilier. 



oppose all tli' I to the same piano 



(Art. -iil, ; next, let them be all trm. so as to have 



